Method and apparatus for transmitting channel state information in wireless communication system

ABSTRACT

The present invention relates to a wireless communication system. According to one embodiment of the present invention, a method for transmitting, by a terminal, channel state information (CSI) in a wireless communication system comprises the steps of: subsampling a code book for four antenna ports; and feeding back the CSI on the basis of the subsampled code book, wherein the CSI includes a rank indicator (RI) reported together with a precoding type indicator (PTI), and if the RI is greater than 2, the PTI is set to one.

TECHNICAL FIELD

The present invention relates to a wireless communication system, andmore particularly, to a method and apparatus for transmitting channelstate information using subsampling of a codebook in a wirelesscommunication system.

BACKGROUND ART

A 3rd generation partnership project long term evolution (3GPP LTE)communication system will be described below as an exemplary mobilecommunication system to which the present invention is applicable.

FIG. 1 is a diagram schematically showing a network structure of anevolved universal mobile telecommunications system (E-UMTS) as anexemplary radio communication system. The E-UMTS system has evolved fromthe conventional UMTS system and basic standardization thereof iscurrently underway in the 3GPP. The E-UMTS may be generally referred toas a long term evolution (LTE) system. For details of the technicalspecifications of the UMTS and E-UMTS, refer to Release 7 and Release 8of “3rd generation partnership project; technical specification groupradio access network”.

Referring to FIG. 1, the E-UMTS includes a user equipment (UE), eNBs (oreNode Bs or base stations), and an access gateway (AG) which is locatedat an end of a network (E-UTRAN) and connected to an external network.The eNBs may simultaneously transmit multiple data streams for abroadcast service, a multicast service, and/or a unicast service.

One or more cells may exist per eNB. A cell is set to use one ofbandwidths of 1.25, 2.5, 5, 10, 15, and 20 MHz to provide a downlink oruplink transport service to several UEs. Different cells may be set toprovide different bandwidths. The eNB controls data transmission andreception for a plurality of UEs. The eNB transmits downlink schedulinginformation with respect to downlink data to notify a corresponding UEof a time/frequency domain in which data is to be transmitted, coding,data size, and hybrid automatic repeat and request (HARQ)-relatedinformation. In addition, the eNB transmits uplink schedulinginformation with respect to UL data to a corresponding UE to inform theUE of an available time/frequency domain, coding, data size, andHARQ-related information. An interface for transmitting user traffic orcontrol traffic may be used between eNBs. A core network (CN) mayinclude the AG, a network node for user registration of the UE, and thelike. The AG manages mobility of a UE on a tracking area (TA) basis,wherein one TA includes a plurality of cells.

Although radio communication technology has been developed up to LTEbased on wideband code division multiple access (WCDMA), the demands andexpectations of users and providers continue to increase. In addition,since other radio access technologies continue to be developed, newtechnology is required to secure competitiveness in the future. Forexample, decrease of cost per bit, increase of service availability,flexible use of a frequency band, simple structure, open interface, andsuitable power consumption by a UE are required.

Multiple-input multiple-output (MIMO) technology refers to a method forenhancing transmission and receiving data efficiency by employingmultiple transmit antennas and multiple receive antennas instead of onetransmit antenna and one receive antenna. That is, the MIMO technologyenhances capacity or improves performance using multiple antennas in atransmitting end or a receiving end of a wireless communication system.The MIMO technology may also be referred to as multiple antennatechnology.

In order to support multiple antenna transmission, a precoding matrixfor appropriately distributing transmitted information according to achannel situation and so on can be applied to each antenna.

DISCLOSURE Technical Problem

An object of the present invention devised to solve the problem lies ina method and apparatus for transmitting channel state information in awireless communication system.

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

Technical Solution

The object of the present invention can be achieved by providing amethod for transmitting channel state information (CSI) by a userequipment in a wireless communication system, the method includingsubsampling a codebook for a 4 antenna port, and feeding back CSI basedon the subsampled codebook, wherein the CSI includes a rank indicator(RI) reported together with a precoding type indicator (PTI), and whenthe RI is greater than 2, the PTI is set to 1.

In another aspect of the present invention, provided herein is a userequipment for transmitting channel state information (CSI) in a wirelesscommunication system, the user equipment including a radio frequency(RF) unit, and a processor, wherein the processor is configured tosubsample a codebook for a 4 antenna port and to feedback CSI based onthe subsampled codebook, the CSI includes a rank indicator (RI) reportedtogether with a precoding type indicator (PTI), and when the RI isgreater than 2, the PTI is set to 1.

The following features may be commonly applied to the above embodimentsof the present invention.

The RI may be set to one of natural numbers equal to or less than 4

The CSI may be transmitted using physical uplink control channel mode2-1 for reporting a single precoding matrix indicator (PMI) and asubband channel quality indicator (CQI).

When the RI is greater than 2, the subsampled codebook may include afirst precoding matrix with an index 0, a third precoding matrix with anindex 2, a ninth precoding matrix with an index 8, and an eleventhprecoding matrix with an index 10.

The subsampling may include subsampling the codebook for the 4 antennaport according to 2I_(PMI2)+4·└I_(PMI2)/2┘, and the IPMI2 may indicatean index of a precoding matrix with one of 0 to 3.

CSI configuration information for report of the CSI may be received.

The CSI configuration information may be transmitted using radioresource control (RRC) signaling.

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

Advantageous Effects

According to embodiments of the present invention, a method andapparatus for effectively transmitting channel state information usingsubsampling of a codebook in a wireless communication system isprovided.

It will be appreciated by persons skilled in the art that that theeffects that could be achieved with the present invention are notlimited to what has been particularly described hereinabove and otheradvantages of the present invention will be more clearly understood fromthe following detailed description taken in conjunction with theaccompanying drawings.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, illustrate embodiments of the inventionand together with the description serve to explain the principle of theinvention.

In the drawings:

FIG. 1 is a diagram schematically showing a network structure of anevolved universal mobile telecommunications system (E-UMTS) as anexemplary radio communication system;

FIG. 2 is a diagram illustrating a control plane and a user plane of aradio interface protocol between a UE and an evolved universalterrestrial radio access network (E-UTRAN) based on a 3rd generationpartnership project (3GPP) radio access network standard;

FIG. 3 is a diagram showing physical channels used in a 3GPP system anda general signal transmission method using the same;

FIG. 4 is a diagram illustrating an example of the structure of a radioframe used in a long term evolution (LTE) system;

FIG. 5 is a diagram illustrating a control channel included in a controlregion of a subframe in a downlink radio frame;

FIG. 6 is a diagram illustrating an uplink subframe structure used in anLTE system;

FIG. 7 illustrates the configuration of a typical multiple inputmultiple output (MIMO) communication system;

FIGS. 8 to 11 illustrate periodic reporting of channel state information(CSI);

FIGS. 12 and 13 illustrate an exemplary process for periodicallyreporting CSI when a non-hierarchical codebook is used;

FIG. 14 is a diagram illustrating periodic reporting of CSI when ahierarchical codebook is used;

FIG. 15 is a diagram illustrating an example of submode A of PUCCHfeedback mode 1-1;

FIG. 16 illustrates PUCCH feedback mode 2-1 according to a PTI value;

FIG. 17 illustrates a submode B when a new codebook is applied;

FIG. 18 illustrates PUCCH feedback mode 2-1 according to a PTI value;

FIG. 19 illustrates an example of PUCCH feedback mode 2-1 in ranks 3 and4;

FIG. 20 illustrates an example of PUCCH feedback mode 2-1 in ranks 3 and4;

FIG. 21 is a flowchart of a method for transmitting channel stateinformation according to an embodiment of the present invention; and

FIG. 22 is a diagram illustrating a BS and a UE to which an embodimentof the present invention is applicable.

BEST MODE

Hereinafter, the structures, operations, and other features of thepresent invention will be understood readily from the embodiments of thepresent invention, examples of which are described with reference to theaccompanying drawings. The embodiments which will be described below areexamples in which the technical features of the present invention areapplied to a 3GPP system.

Although the embodiments of the present invention will be describedbased on an LTE system and an LTE-Advanced (LTE-A) system, the LTEsystem and the LTE-A system are only exemplary and the embodiments ofthe present invention can be applied to all communication systemscorresponding to the aforementioned definition. In addition, althoughthe embodiments of the present invention will herein be described basedon Frequency Division Duplex (FDD) mode, the FDD mode is only exemplaryand the embodiments of the present invention can easily be modified andapplied to Half-FDD (H-FDD) mode or Time Division Duplex (TDD) mode.

FIG. 2 is a view illustrating structures of a control plane and a userplane of a radio interface protocol between a UE and an E-UTRAN based onthe 3GPP radio access network specification. The control plane refers toa path through which control messages used by a User Equipment (UE) anda network to manage a call are transmitted. The user plane refers to apath through which data generated in an application layer, e.g. voicedata or Internet packet data, is transmitted.

A physical layer of a first layer provides an information transferservice to an upper layer using a physical channel. The physical layeris connected to a Medium Access Control (MAC) layer of an upper layervia a transport channel. Data is transported between the MAC layer andthe physical layer via the transport channel. Data is also transportedbetween a physical layer of a transmitting side and a physical layer ofa receiving side via a physical channel. The physical channel uses timeand frequency as radio resources. Specifically, the physical channel ismodulated using an Orthogonal Frequency Division Multiple Access (OFDMA)scheme in downlink and is modulated using a Single-Carrier FrequencyDivision Multiple Access (SC-FDMA) scheme in uplink.

A MAC layer of a second layer provides a service to a Radio Link Control(RLC) layer of an upper layer via a logical channel. The RLC layer ofthe second layer supports reliable data transmission. The function ofthe RLC layer may be implemented by a functional block within the MAC. APacket Data Convergence Protocol (PDCP) layer of the second layerperforms a header compression function to reduce unnecessary controlinformation for efficient transmission of an Internet Protocol (IP)packet such as an IPv4 or IPv6 packet in a radio interface having arelatively narrow bandwidth.

A Radio Resource Control (RRC) layer located at the bottommost portionof a third layer is defined only in the control plane. The RRC layercontrols logical channels, transport channels, and physical channels inrelation to configuration, re-configuration, and release of radiobearers. The radio bearers refer to a service provided by the secondlayer to transmit data between the UE and the network. To this end, theRRC layer of the UE and the RRC layer of the network exchange RRCmessages. The UE is in an RRC connected mode if an RRC connection hasbeen established between the RRC layer of the radio network and the RRClayer of the UE. Otherwise, the UE is in an RRC idle mode. A Non-AccessStratum (NAS) layer located at an upper level of the RRC layer performsfunctions such as session management and mobility management.

One cell of an eNB is set to use one of bandwidths such as 1.25, 2.5, 5,10, 15, and 20 MHz to provide a downlink or uplink transmission serviceto a plurality of UEs. Different cells may be set to provide differentbandwidths.

Downlink transport channels for data transmission from a network to a UEinclude a Broadcast Channel (BCH) for transmitting system information, aPaging Channel (PCH) for transmitting paging messages, and a downlinkShared Channel (SCH) for transmitting user traffic or control messages.Traffic or control messages of a downlink multicast or broadcast servicemay be transmitted through the downlink SCH or may be transmittedthrough an additional downlink Multicast Channel (MCH). Meanwhile,uplink transport channels for data transmission from the UE to thenetwork include a Random Access Channel (RACH) for transmitting initialcontrol messages and an uplink SCH for transmitting user traffic orcontrol messages. Logical channels, which are located at an upper levelof the transport channels and are mapped to the transport channels,include a Broadcast Control Channel (BCCH), a Paging Control Channel(PCCH), a Common Control Channel (CCCH), a Multicast Control Channel(MCCH), and a Multicast Traffic Channel (MTCH).

FIG. 3 is a view illustrating physical channels used in a 3GPP systemand a general signal transmission method using the same.

A UE performs initial cell search such as establishment ofsynchronization with an eNB when power is turned on or the UE enters anew cell (step S301). The UE may receive a Primary SynchronizationChannel (P-SCH) and a Secondary Synchronization Channel (S-SCH) from theeNB, establish synchronization with the eNB, and acquire informationsuch as a cell identity (ID). Thereafter, the UE may receive a physicalbroadcast channel from the eNB to acquire broadcast information withinthe cell. Meanwhile, the UE may receive a Downlink Reference Signal (DLRS) in the initial cell search step to confirm a downlink channel state.

Upon completion of initial cell search, the UE may receive a PhysicalDownlink Control Channel (PDCCH) and a Physical Downlink Shared Channel(PDSCH) according to information carried on the PDCCH to acquire moredetailed system information (step S302).

Meanwhile, if the UE initially accesses the eNB or if radio resourcesfor signal transmission are not present, the UE may perform a randomaccess procedure (steps S303 to S306) with respect to the eNB. To thisend, the UE may transmit a specific sequence through a Physical RandomAccess Channel (PRACH) as a preamble (steps S303 and S305), and receivea response message to the preamble through the PDCCH and the PDSCHcorresponding thereto (steps S304 and S306). In the case of acontention-based RACH, a contention resolution procedure may beadditionally performed.

The UE which performs the above procedures may receive a PDCCH/PDSCH(step S307) and transmit a Physical Uplink Shared Channel(PUSCH)/Physical Uplink Control Channel (PUCCH) (step S308) according toa general uplink/downlink signal transmission procedure. Especially, theUE receives Downlink Control Information (DCI) through the PDCCH. TheDCI includes control information such as resource allocation informationfor the UE and has different formats according to use purpose.

Meanwhile, control information, transmitted by the UE to the eNB throughuplink or received by the UE from the eNB through downlink, includes adownlink/uplink ACKnowledgment/Negative ACKnowledgment (ACK/NACK)signal, a Channel Quality Indicator (CQI), a Precoding Matrix Index(PMI), a Rank Indicator (RI), and the like. In the case of the 3GPP LTEsystem, the UE may transmit control information such as CQI/PMI/RIthrough the PUSCH and/or the PUCCH.

FIG. 4 is a view illustrating the structure of a radio frame used in anLTE system.

Referring to FIG. 4, the radio frame has a length of 10 ms (327200 Ts)and includes 10 equally-sized subframes. Each of the subframes has alength of 1 ms and includes two slots. Each of the slots has a length of0.5 ms (15360 Ts). In this case, Ts denotes sampling time and isrepresented by Ts=1/(15 kHz×2048)=3.2552×10−8 (about 33 ns). Each slotincludes a plurality of OFDM symbols in a time domain and includes aplurality of Resource Blocks (RBs) in a frequency domain. In the LTEsystem, one resource block includes 12 subcarriers×7 (or 6) OFDMsymbols. A Transmission Time Interval (TTI), which is a unit time fordata transmission, may be determined in units of one or more subframes.The above-described structure of the radio frame is purely exemplary andvarious modifications may be made in the number of subframes included ina radio frame, the number of slots included in a subframe, or the numberof OFDM symbols included in a slot.

FIG. 5 is a view illustrating control channels contained in a controlregion of one subframe in a downlink radio frame.

Referring to FIG. 5, one subframe includes 14 OFDM symbols. The first tothird ones of the 14 OFDM symbols may be used as a control region andthe remaining 13 to 11 OFDM symbols may be used as a data region,according to subframe configuration. In FIG. 5, R1 to R4 representreference signals (RSs) or pilot signals for antennas 0 to 3,respectively. The RSs are fixed to a predetermined pattern within thesubframe irrespective of the control region and the data region. Controlchannels are allocated to resources to which the RS is not allocated inthe control region. Traffic channels are allocated to resources, towhich the RS is not allocated, in the data region. The control channelsallocated to the control region include a Physical Control FormatIndicator Channel (PCFICH), a Physical Hybrid-ARQ Indicator Channel(PHICH), a Physical Downlink Control Channel (PDCCH), etc.

The PCFICH, physical control format indicator channel, informs a UE ofthe number of OFDM symbols used for the PDCCH per subframe. The PCFICHis located in the first OFDM symbol and is established prior to thePHICH and the PDCCH. The PCFICH is comprised of 4 Resource ElementGroups (REGs) and each of the REGs is distributed in the control regionbased on a cell ID. One REG includes 4 Resource Elements (REs). The REindicates a minimum physical resource defined as one subcarrier×one OFDMsymbol. The PCFICH value indicates values of 1 to 3 or values of 2 to 4depending on bandwidth and is modulated by Quadrature Phase Shift Keying(QPSK).

The PHICH, physical Hybrid-ARQ indicator channel, is used to transmit aHARQ ACK/NACK signal for uplink transmission. That is, the PHICHindicates a channel through which downlink ACK/NACK information foruplink HARQ is transmitted. The PHICH includes one REG and iscell-specifically scrambled. The ACK/NACK signal is indicated by 1 bitand is modulated by Binary Phase Shift Keying (BPSK). The modulatedACK/NACK signal is spread by a Spreading Factor (SF)=2 or 4. A pluralityof PHICHs mapped to the same resource constitutes a PHICH group. Thenumber of PHICHs multiplexed to the PHICH group is determined dependingon the number of SFs. The PHICH (group) is repeated three times toobtain diversity gain in a frequency domain and/or a time domain.

The PDCCH, physical downlink control channel, is allocated to the firstn OFDM symbols of a subframe. In this case, n is an integer greater than1 and is indicated by the PCFICH. The PDCCH is comprised of one or moreControl Channel Elements (CCEs). The PDCCH informs each UE or UE groupof information associated with resource allocation of a Paging Channel(PCH) and a Downlink-Shared Channel (DL-SCH), uplink scheduling grant,Hybrid Automatic Repeat Request (HARQ) information, etc. Therefore, aneNB and a UE transmit and receive data other than specific controlinformation or specific service data through the PDSCH.

Information indicating to which UE or UEs PDSCH data is to betransmitted, information indicating how UEs are to receive PDSCH data,and information indicating how UEs are to perform decoding are containedin the PDCCH. For example, it is assumed that a specific PDCCH isCRC-masked with a Radio Network Temporary Identity (RNTI) “A” andinformation about data, that is transmitted using radio resources “B”(e.g., frequency location) and transport format information “C” (e.g.,transmission block size, modulation scheme, coding information, etc.),is transmitted through a specific subframe. In this case, a UE locatedin a cell monitors the PDCCH using its own RNTI information. If one ormore UEs having the RNTI ‘A’ are present, the UEs receive the PDCCH andreceive the PDSCH indicated by ‘B’ and ‘C’ through the received PDCCHinformation.

FIG. 6 illustrates the structure of an uplink subframe used in the LTEsystem.

Referring to FIG. 6, an uplink subframe is divided into a region towhich a PUCCH is allocated to transmit control information and a regionto which a PUSCH is allocated to transmit user data. The PUSCH isallocated to the middle of the subframe, whereas the PUCCH is allocatedto both ends of a data region in the frequency domain. The controlinformation transmitted on the PUCCH includes an ACK/NACK, a CQIrepresenting a downlink channel state, an RI for Multiple Input andMultiple Output (MIMO), a Scheduling Request (SR) indicating a requestfor allocation of uplink resources, etc. A PUCCH of a UE occupies one RBin a different frequency in each slot of a subframe. That is, two RBsallocated to the PUCCH frequency-hop over the slot boundary.Particularly, FIG. 6 illustrates an example in which PUCCHs for m=0,m=1, m=2, and m=3 are allocated to a subframe.

Hereinafter, a MIMO system will be described. MIMO refers to a method ofusing multiple transmission antennas and multiple reception antennas toimprove data transmission/reception efficiency. Namely, a plurality ofantennas is used at a transmitting end or a receiving end of a wirelesscommunication system so that capacity can be increased and performancecan be improved. MIMO may also be referred to as ‘multi-antenna’ in thisdisclosure.

MIMO System

MIMO technology does not depend on a single antenna path in order toreceive a whole message. Instead, MIMO technology collects datafragments received via several antennas, merges the data fragments, andforms complete data. The use of MIMO technology can increase systemcoverage while improving data transfer rate within a cell area of aspecific size or guaranteeing a specific data transfer rate. MIMOtechnology can be widely used in mobile communication terminals andrelay nodes. MIMO technology can overcome the limitations of therestricted amount of transmission data of single antenna based mobilecommunication systems.

The configuration of a general MIMO communication system is shown inFIG. 7. A transmitting end is equipped with NT transmission (Tx)antennas and a receiving end is equipped with NR reception (Rx)antennas. If a plurality of antennas is used both at the transmittingend and at the receiving end, theoretical channel transmission capacityincreases unlike the case where only either the transmitting end or thereceiving end uses a plurality of antennas. Increase in channeltransmission capacity is proportional to the number of antennas, therebyimproving transfer rate and frequency efficiency. If a maximum transferrate using a signal antenna is Ro, a transfer rate using multipleantennas can be theoretically increased by the product of the maximumtransfer rate Ro by a rate increment Ri. The rate increment Ri isrepresented by the following equation 1 where Ri is the smaller of NTand NR.

R _(i)=min(N _(T) ,N _(R))  [Equation 1]

For example, in a MIMO communication system using four Tx antennas andfour Rx antennas, it is possible to theoretically acquire a transferrate four times that of a single antenna system. After theoreticalincrease in the capacity of the MIMO system was first demonstrated inthe mid-1990s, various techniques for substantially improving datatransfer rate have been under development. Several of these techniqueshave already been incorporated into a variety of wireless communicationstandards including, for example, 3rd generation mobile communicationand next-generation wireless local area networks.

Active research up to now related to MIMO technology has focused upon anumber of different aspects, including research into information theoryrelated to MIMO communication capacity calculation in various channelenvironments and in multiple access environments, research into wirelesschannel measurement and model derivation of MIMO systems, and researchinto space-time signal processing technologies for improvingtransmission reliability and transfer rate.

To describe a communication method in a MIMO system in detail, amathematical model thereof is given below. As shown in FIG. 7, it isassumed that NT Tx antennas and NR Rx antennas are present. In the caseof a transmission signal, a maximum number of transmittable pieces ofinformation is NT under the condition that NT Tx antennas are used, sothat transmission information can be represented by a vector representedby the following equation 2:

S=[S ₁ ,S ₂ , . . . ,S _(N) _(T) ]^(T)  [Equation 2]

Meanwhile, individual transmission information pieces S₁, S₂, . . . ,S_(N) _(T) may have different transmission powers. In this case, if theindividual transmission powers are denoted by P₁, P₂, . . . , P_(N) _(T), transmission information having adjusted transmission powers can berepresented by a vector shown in the following equation 3:

ŝ=[ŝ ₁ ,ŝ ₂ , . . . ,ŝ _(N) _(T) ]T=[P ₁ s ₁ ,P ₂ s ₂ , . . . ,P _(N)_(T) s _(N) _(T) ]^(T)  [Equation 3]

The transmission power-controlled transmission information vector ŝ maybe expressed as follows, using a diagonal matrix P of a transmissionpower:

$\begin{matrix}{\hat{s} = {{\begin{bmatrix}P_{1} & \; & \; & 0 \\\; & P_{2} & \; & \; \\\; & \; & \ddots & \; \\0 & \; & \; & P_{N_{T}}\end{bmatrix}\begin{bmatrix}s_{1} \\s_{2} \\\vdots \\s_{N_{T}}\end{bmatrix}} = {Ps}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

NT transmission signals x₁, x₂, . . . , x_(N) _(T) to be actuallytransmitted may be configured by multiplying the transmissionpower-controlled information vector S by a weight matrix W. In thiscase, the weight matrix is adapted to properly distribute transmissioninformation to individual antennas according to transmission channelsituations. The transmission signals x₁, x₂, . . . , x_(N) _(T) can berepresented by the following Equation 5 using a vector X. In Equation 5,W_(ij) is a weight between the i-th Tx antenna and the j-th informationand W is a weight matrix, which may also be referred to as a precodingmatrix.

$\begin{matrix}\begin{matrix}{x = \begin{bmatrix}x_{1} \\x_{2} \\\vdots \\x_{i} \\\vdots \\x_{N_{T}}\end{bmatrix}} \\{= {\begin{bmatrix}w_{11} & w_{12} & \ldots & w_{1N_{T}} \\w_{21} & w_{22} & \ldots & w_{2N_{T}} \\\vdots & \vdots & \ddots & \vdots \\w_{i\; 1} & w_{i\; 2} & \ldots & w_{i\; N_{T}} \\\vdots & \vdots & \ddots & \vdots \\w_{N_{T}1} & w_{N_{T}2} & \ldots & w_{N_{T}N_{T}}\end{bmatrix}\begin{bmatrix}{\hat{s}}_{1} \\{\hat{s}}_{2} \\\vdots \\{\hat{s}}_{j} \\\vdots \\{\hat{s}}_{N_{T}}\end{bmatrix}}} \\{= {W\hat{s}}} \\{= {WPs}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

Generally, the physical meaning of a rank of a channel matrix may be amaximum number of different pieces of information that can betransmitted in a given channel. Accordingly, since the rank of thechannel matrix is defined as the smaller of the number of rows orcolumns, which are independent of each other, the rank of the matrix isnot greater than the number of rows or columns. A rank of a channelmatrix H, rank(H), is restricted as follows.

rank(H)≦min(N _(T) ,N _(R))  [Equation 6]

Each unit of different information transmitted using MIMO technology isdefined as a ‘transmission stream’ or simply ‘stream’. The ‘stream’ maybe referred to as a ‘layer’. The number of transmission streams is notgreater than a rank of a channel which is a maximum number of differentpieces of transmittable information. Accordingly, the channel matrix Hmay be indicted by the following Equation 7:

# of streams≦rank(H)≦min(N _(T) ,N _(R))  [Equation 7]

where ‘# of streams’ denotes the number of streams. It should be notedthat one stream may be transmitted through one or more antennas.

There may be various methods of allowing one or more streams tocorrespond to multiple antennas. These methods may be described asfollows according to types of MIMO technology. The case where one streamis transmitted via multiple antennas may be called spatial diversity,and the case where multiple streams are transmitted via multipleantennas may be called spatial multiplexing. It is also possible toconfigure a hybrid of spatial diversity and spatial multiplexing.

CSI Feedback

Now, a description of a Channel State Information (CSI) report is given.In the current LTE standard, a MIMO transmission scheme is categorizedinto open-loop MIMO operated without CSI and closed-loop MIMO operatedbased on CSI. Especially, according to the closed-loop MIMO system, eachof the eNB and the UE may be able to perform beamforming based on CSI toobtain a multiplexing gain of MIMO antennas. To obtain CSI from the UE,the eNB allocates a PUCCH or a PUSCH to command the UE to feed back CSIfor a downlink signal.

CSI is divided into three types of information: a Rank Indicator (RI), aPrecoding Matrix Index (PMI), and a Channel Quality Indicator (CQI).First, RI is information on a channel rank as described above andindicates the number of streams that can be received via the sametime-frequency resource. Since RI is determined by long-term fading of achannel, it may be generally fed back at a cycle longer than that of PMIor CQI.

Second, PMI is a value reflecting a spatial characteristic of a channeland indicates a precoding matrix index of the eNB preferred by the UEbased on a metric of Signal-to-Interference plus Noise Ratio (SINR).Lastly, CQI is information indicating the strength of a channel andindicates a reception SINR obtainable when the eNB uses PMI.

In an evolved communication system such as an LTE-A system, multi-userdiversity using Multi-User MIMO (MU-MIMO) is additionally obtained.Since interference between UEs multiplexed in an antenna domain existsin the MU-MIMO scheme, CSI accuracy may greatly affect not onlyinterference of a UE that has reported CSI but also interference ofother multiplexed UEs. Hence, in order to correctly perform MU-MIMOoperation, it is necessary to report CSI having accuracy higher thanthat of a Single User-MIMO (SU-MIMO) scheme.

Accordingly, LTE-A standard has determined that a final PMI should beseparately designed into W1, which a long-term and/or wideband PMI, andW2, which is a short-term and/or subband PMI.

An example of a hierarchical codebook transform scheme configuring onefinal PMI from among W1 and W2 may use a long-term covariance matrix ofa channel as indicated in Equation 8:

W=norm(W1W2)  [Equation 8]

In Equation 8, W2 of a short-term PMI indicates a codeword of a codebookconfigured to reflect short-term channel information, W denotes acodeword of a final codebook, and norm(A) indicates a matrix in which anorm of each column of a matrix A is normalized to 1.

The detailed configurations of W1 and W2 are shown in Equation 9:

$\begin{matrix}{{{W\; 1(i)} = \begin{bmatrix}X_{i} & 0 \\0 & X_{i}\end{bmatrix}},{{{where}\mspace{14mu} X_{i}\mspace{14mu} {is}\mspace{14mu} {{Nt}/2}\mspace{14mu} {by}\mspace{14mu} M\mspace{14mu} {{matrix}.W}\; 2(j)} = {\overset{\overset{r\mspace{14mu} {columns}}{}}{\begin{bmatrix}e_{M}^{k} & e_{M}^{l} & e_{M}^{m} \\{\alpha_{j}e_{M}^{k}} & {\beta_{j}e_{M}^{l}} & \overset{\ldots}{\gamma_{j}e_{M}^{m}}\end{bmatrix}}\mspace{14mu} \left( {{{if}\mspace{14mu} {rank}} = r} \right)}},{{{where}\mspace{14mu} 1} \leq k},l,{m \leq {M\mspace{14mu} {and}\mspace{14mu} k}},l,{m\mspace{14mu} {are}\mspace{14mu} {{integer}.}}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

where Nt is the number of Tx antennas, M is the number of columns of amatrix Xi, indicating that the matrix Xi includes a total of M candidatecolumn vectors. eMk, eMl, and eMm denote k-th, l-th, and m-th columnvectors of the matrix Xi in which only k-th, l-th, and m-th elementsamong M elements are 0 and the other elements are 0, respectively.α_(j), β_(j), and γ_(j) are complex values each having a unit norm andindicate that, when the k-th, l-th, and m-th column vectors of thematrix Xi are selected, phase rotation is applied to the column vectors.At this time, i is an integer greater than 0, denoting a PMI indexindicating W1 and j is an integer greater than 0, denoting a PMI indexindicating W2.

In Equation 9, the codebook configurations are designed to reflectchannel correlation properties generated when cross polarized antennasare used and when a space between antennas is dense, for example, when adistance between adjacent antennas is less than a half of signalwavelength. The cross polarized antennas may be categorized into ahorizontal antenna group and a vertical antenna group. Each antennagroup has the characteristic of a Uniform Linear Array (ULA) antenna andthe two groups are co-located.

Accordingly, a correlation between antennas of each group hascharacteristics of the same linear phase increment and a correlationbetween antenna groups has characteristics of phase rotation.Consequently, since a codebook is a value obtained by quantizing achannel, it is necessary to design a codebook such that characteristicsof a channel are reflected. For convenience of description, a rank-1codeword generated by the aforementioned configurations is shown asfollows:

$\begin{matrix}{{W\; 1(i)*W\; 2(j)} = \begin{bmatrix}{X_{i}(k)} \\{\alpha_{j}{X_{i}(k)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

In Equation 10, a codeword is expressed as a vector of N_(T)×1 (where NTis the number of Tx antennas) and is structured with an upper vectorX_(i)(k) and a lower vector α_(j)X_(i)(k) which show correlationcharacteristics of a horizontal antenna group and a vertical antennagroup, respectively. X_(i)(k) is preferably expressed as a vector havingthe characteristics of linear phase increment by reflecting thecharacteristics of a correlation between antennas of each antenna groupand may be a DFT matrix as a representative example.

As described above, CSI in the LTE system includes, but is not limitedto, CQI, PMI, and RI. According to transmission mode of each UE, all orsome of the CQI, PMI, and RI is transmitted. Periodic transmission ofCSI is referred to as periodic reporting and transmission of CSI at therequest of an eNB is referred to as aperiodic reporting. In aperiodicreporting, a request bit included in uplink scheduling informationtransmitted by the eNB is transmitted to the UE. Then, the UE transmitsCSI considering transmission mode thereof to the eNB through an uplinkdata channel (PUSCH). In periodic reporting, a period of CSI and anoffset at the period are signaled in the unit of subframes by asemi-static scheme through a higher-layer signal per UE. The UEtransmits CSI considering transmission mode to the eNB through an uplinkcontrol channel (PUCCH). If there is uplink data in a subframe in whichCSI is transmitted, the CSI is transmitted through an uplink datachannel (PUSCH) together with the uplink data. The eNB transmitstransmission timing information suitable for each UE to the UE inconsideration of a channel state of each UE and a UE distributedsituation in a cell. The transmission timing information includes aperiod and an offset necessary for transmitting CSI and may betransmitted to each UE through an RRC message.

FIGS. 8 to 11 illustrate periodic reporting of CSI in an LTE system.

Referring to FIG. 8, there are four CQI reporting modes in the LTEsystem. Specifically, the CQI reporting modes may be divided into modesin a WideBand (WB) CQI and modes in a SubBand (SB) CQI according to CQIfeedback type. The CQI reporting mode may also be divided into modes ina No PMI and modes in a single PMI depending on whether a PMI istransmitted or not. Each UE is informed of information comprised of aperiod and an offset through RRC signaling in order to periodicallyreport CQI.

FIG. 9 illustrates an example of transmitting CSI when a UE receivesinformation indicating {a period ‘5’ and an offset ‘1’} throughsignaling. Referring to FIG. 9, upon receiving the informationindicating the period ‘5’ and offset ‘1’, the UE transmits CSI in theunit of 5 subframes with an offset of one subframe in ascending order ofa subframe index counted from 0 starting from the first subframe.Although the CSI is transmitted basically through a PUCCH, if a PUSCHfor data transmission is present at the same transmission time point,the CSI is transmitted through the PUSCH together with data. Thesubframe index is given as a combination of a system frame number (or aradio frame index) nf and a slot index ns (0 to 19). Since one subframeincludes two slots, the subframe index may be defined as10×nf+floor(ns/2) wherein floor( ) indicates the floor function.

CQI transmission types include a type of transmitting a WB CQI only anda type of transmitting both a WB CQI and an SB CQI. In the type oftransmitting a WB CQI only, CQI information for all bands is transmittedin subframes corresponding to every CQI transmission period. Meanwhile,in the case in which PMI information should also be transmittedaccording to the PMI feedback type as illustrated in FIG. 8, the PMIinformation is transmitted together with the CQI information. In thetype of transmitting both a WB CQI and an SB CQI, the WB CQI and SB CQIare alternately transmitted.

FIG. 10 illustrates a system in which a system bandwidth consists of 16RBs. It is assumed that the system bandwidth includes two BandwidthParts (BPs) BP0 and BP1 each consisting of two SubBands (SBs) SB0 andSB1 and each SB includes 4 RBs. The above assumption is exemplary andthe number of BPs and the size of each SB may vary with the size of thesystem bandwidth. The number of SBs constituting each BP may differaccording to the number of RBs, the number of BPs, and the size of eachSB.

In the CQI transmission type of transmitting both a WB CQI and an SBCQI, the WB CQI is transmitted in the first CQI transmission subframeand an SB CQI of the better SB state of SB0 and SB1 in BP0 istransmitted in the next CQI transmission subframe together with and anindex of the corresponding SB (e.g. Subband Selection Indicator (SSI).Thereafter, an SB CQI of the better SB state of SB0 and SB1 in BP1 andan index of the corresponding SB are transmitted in the next CQItransmission subframe. Thus, CQI of each BP is sequentially transmittedafter transmission of the WB CQI. The CQI of each BP may be sequentiallytransmitted once to four times during the interval between transmissionintervals of two WB CQIs. For example, if the CQI of each BP istransmitted once during the time interval between two WB CQIs, CQIs maybe transmitted in the order of WB CQI

BP0 CQI

BP1 CQI

WB CQI. If the CQI of each BP is transmitted four times during the timeinterval between two WB CQIs, CQIs may be transmitted in the order of WBCQI

BP0 CQI

BP1 CQI

BP0 CQI

BP1 CQI

BP0 CQI

BP1 CQI

BP0 CQI

BP1 CQI

WB CQI. Information as to how many times each BP CQI is transmitted issignaled by a higher layer (RRC layer).

FIG. 11(a) illustrates an example of transmitting both a WB CQI and anSB CQI when a UE receives information indicating {period ‘5’ and offset‘1’} through signaling. Referring to FIG. 11(a), a CQI may betransmitted only in subframes corresponding to the signaled period andoffset regardless of type. FIG. 11(b) illustrates an example oftransmitting an RI in addition to the example shown in FIG. 11(a). TheRI may be signaled as a combination of a multiple of a WB CQItransmission period and an offset at the transmission period from ahigher layer (e.g. RRC layer). The offset of the RI is signaled using avalue relative to the offset of a CQI. For example, if the offset of theCQI is ‘1’ and the offset of the RI is ‘0’, the RI has the same offsetas the CQI. The offset value of the RI is defined as 0 or a negativenumber. More specifically, it is assumed in FIG. 11(b) that, in anenvironment identical to that of FIG. 11(a), an RI transmission periodis a multiple of 1 of the WB CQI transmission period and the RI offsetis ‘−1’. Since the RS transmission period is a multiple of 1 of the WBCQI transmission period, the RS transmission period and the WB CQItransmission period are substantially the same. Since the offset of theRI is ‘−1’, the RI is transmitted based upon the value ‘−1’ (i.e.subframe index 0) relative to the offset ‘1’ of the CQI in FIG. 11(a).If the offset of the RI is ‘0’, the transmission subframes of the WB CQIand RI overlap. In this case, the WB CQI is dropped and the RI istransmitted.

FIG. 12 illustrates CSI feedback in the case of Mode 1-1 of FIG. 8.

Referring to FIG. 12, CSI feedback is comprised of two types of reportcontent, i.e. transmission of Report 1 and transmission of Report 2.More specifically, an RI is transmitted through Report 1 and a WB PMIand a WB CQI are transmitted through Report 2. Report 2 is transmittedin subframe indexes satisfying(10*nf+floor(ns/2)−Noffset,CQI)mod(Npd)=0. Noffset,CQI indicates anoffset for PMI/CQI transmission shown in FIG. 9. In FIG. 12,Noffset,CQI=1. Npd illustrates an interval of subframes betweencontiguous Reports 2 and the case of Npd=2 is illustrated in FIG. 12.Report 1 is transmitted in subframe indexes satisfying(10*nf+floor(ns/2)−Noffset,CQI−Noffset,RI)mod(MRI*Npd)=0. MRI isdetermined by higher layer signaling. Noffset,RI denotes a relativeoffset value for RI transmission shown in FIG. 11. The case in whichMRI=4 and Noffset,RI=−1 is illustrated in FIG. 12.

FIG. 13 illustrates CSI feedback in the case of Mode 2-1 of FIG. 8.

Referring to FIG. 13, CSI feedback is comprised of three types of reportcontent, i.e. transmission of Report 1, transmission of Report 2, andtransmission of Report 3. More specifically, an RI is transmittedthrough Report 1, a WB PMI and a WB CQI are transmitted through Report2, and an SB CQI and an L-bit Subband Selection Indicator (SSI) aretransmitted through Report 3. Report 2 or Report 3 is transmitted insubframe indexes satisfying (10*nf+floor(ns/2)−Noffset,CQI)mod(Npd)=0.Especially, Report 2 is transmitted in subframe indexes satisfying(10*nf+floor(ns/2)−Noffset,CQI)mod(H*Npd)=0. Accordingly, Report 2 istransmitted at an interval of H*Npd and subframes between contiguousReports are filled with transmission of Report 3. At this time, H equalsto J*K+1 wherein J is the number of BPs. K is a value indicating howmany full cycles will be consecutively performed, wherein the full cycleis a cycle during which a process for selectively transmitting a subbandonce per different BP over all BPs. K is determined by higher layersignaling. The case in which Npd=2, J=3, and K=1 is illustrated in FIG.13. Report 1 is transmitted in subframe indexes satisfying(10*nf+floor(ns/2)−Noff,CQI−Noffset,RI)mod(MRI*(J*K+1)*Npd)=0. The casein which MRI=2 and Noffset,RI=−1 is illustrated in FIG. 13.

FIG. 14 illustrates periodic reporting of CSI which is being discussedin LTE-A. If an eNB includes 8 Tx antennas in Mode 2-1, then a 1-bitindicator, i.e. a Precoder Type Indication (PTI) parameter, isconfigured and periodic reporting modes classified into two typesaccording to the PTI value are considered. In FIG. 14, W1 and W2illustrate hierarchical codebooks described with reference to Equations8 and 9. If both W1 and W2 are determined, a completed type of aprecoding matrix W is determined by combining W1 and W2.

Referring to FIG. 14, in the case of periodic reporting, differentcontents corresponding to Report 1, Report 2, and Report 3 are reportedaccording to different repetition periods. An RI and a 1-bit PTI valueare reported through Report 1. A WB W1 (when PTI=0) or a WB W2 and a WBCQI (when PTI=1) are reported through Report 2. A WB W2 and a WB CQI(when PTI=0) or an SB W2 and an SB CQI (when PTI=1) are reported throughReport 3.

Report 2 and Report 3 are transmitted in subframes (for convenience,referred to as a first subframe set) having subframe indexes satisfying(10*nf+floor(ns/2)−Noffset,CQI) mod (NC)=0 wherein Noffset,CQI is anoffset value for PMI/CQI transmission shown in FIG. 9 and Nc denotes asubframe interval between contiguous Reports 2 or Reports 3. The case inwhich Noffset,CQI=1 and Nc=2 is illustrated in FIG. 14. The firstsubframe set is comprised of subframes having odd-numbered indexes. nfdenotes a system frame number (or radio frame index) and ns denotes aslot index in a radio frame. floor( ) indicates the floor function and‘A mod B’ indicates a remainder obtained by dividing A by B.

Report 2 is located in some subframes in the first subframe set andReport 3 is located in the other subframes. More specifically, Report 2is located in subframes having subframe indexes satisfying(10*nf+floor(ns/2)−Noffset,CQI) mod (H*Nc)=0. Accordingly, Report 2 istransmitted at an interval of H*Nc and one or more first subframesbetween contiguous Reports 2 are filled with transmission of Report 3.If PTI=0, then H=M and M is determined by higher layer signaling. Thecase in which M=2 is illustrated in FIG. 14. If PTI=1, then H=J*K+1, Kis determined by higher layer signaling, and J is the number of BPs. InFIG. 14, J=3 and K=1.

Report 1 is transmitted in subframes having subframe indexes satisfying(10*nf+floor(ns/2)−Noffset,CQI−Noffset,RI) mod (MRI*(J*K+1)*Nc)=0wherein MRI is determined by higher layer signaling. Noffset,RIindicates a relative offset value for an RI. In FIG. 14, MRI=2 andNoffset,RI=−1. The transmission time points of Report 1 and Report 2 donot overlap because Noffset,RI=−1. When a UE calculates RI, W1, and W2,they are associated with each other. For example, W1 and W2 arecalculated depending on RI and W2 is calculated depending on W1. A BSmay be aware of a final W from W1 and W2 when Both Report 2 and Report 3are Reported after Report 1 is Reported.

8 Tx (Transmit Antenna) Codebook

A communication system such as LTE-A further applies multi-userdiversity technology using multi-user MIMO (MU-MIMO). To this end, froma feedback point of view, more enhanced accuracy is required thanbefore. This is because there is an interference channel between UEsthat are multiplexed in an antenna domain of MU-MIMO, and thus theaccuracy of a feedback channel largely affects another multiplexed UE aswell as a UE that transmits feedback. Accordingly, in order to enhancefeedback channel accuracy in LTE-A, a PMI of a 8Tx codebook may bedesigned to be divided into W⁽¹⁾ that is a long term and/or widebandprecoder and W⁽²⁾ that is a short term and/or sub-band precoder.

An equation for one final PMI from two-channel information isrepresented by multiplication of W⁽¹⁾ and W⁽²⁾ as follows.

W=norm(W ⁽¹⁾ W ⁽²⁾)  [Equation 11]

In [Equation 11] above, W is a precoder generated from W⁽¹⁾ and W⁽²⁾,and UE feedbacks the information to a BS. norm(A) refers to a matrixwith a norm normalized to 1 for each column of matrix A.

Detailed configurations of W⁽¹⁾ and W⁽²⁾ in a 8Tx codebook defined inLTE are represented as follows.

$\begin{matrix}{{{W\; 1(i)} = \begin{bmatrix}X_{i} & 0 \\0 & X_{i}\end{bmatrix}},{{{where}\mspace{14mu} X_{i}\mspace{14mu} {is}\mspace{14mu} {{Nt}/2}\mspace{14mu} {by}\mspace{14mu} M\mspace{14mu} {{matrix}.W}\; 2(j)} = {\overset{\overset{r\mspace{14mu} {columns}}{}}{\begin{bmatrix}e_{M}^{k} & e_{M}^{l} & e_{M}^{m} \\{\alpha_{j}e_{M}^{k}} & {\beta_{j}e_{M}^{l}} & \overset{\ldots}{\gamma_{j}e_{M}^{m}}\end{bmatrix}}\mspace{14mu} \left( {{{if}\mspace{14mu} {rank}} = r} \right)}},{{{where}\mspace{14mu} 1} \leq k},l,{m \leq {M\mspace{14mu} {and}\mspace{14mu} k}},l,{m\mspace{14mu} {are}\mspace{14mu} {{integer}.}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

The codewords are designed so as to reflect correlation characteristicsbetween established channels, if cross polarized antennas are arrangeddensely, for example, the distance between adjacent antennas is equal toor less than a half of a signal wavelength. The cross polarized antennasmay be divided into a horizontal antenna group and a vertical antennagroup and the two antenna groups are co-located, each having theproperty of a uniform linear array (ULA) antenna. Therefore, thecorrelations between antennas in each group have the same linear phaseincrement (LPI and LPI) property and the correlation between the antennagroups is characterized by phase rotation.

Since a codebook is eventually quantized values of channels, it isnecessary to design a codebook, reflecting channel characteristicscorresponding to a source. For example, a rank 1 codeword satisfying[Equation 13] may reflect the aforementioned characteristics.

$\begin{matrix}{{W\; 1(i)*W\; 2(j)} = \begin{bmatrix}{X_{i}(k)} \\{\alpha_{j}{X_{i}(k)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

In [Equation 13], a codeword is expressed as an Nt×1 (N_(T) is thenumber of Tx antennas) and the codeword is composed of an upper vectorX_(i)(k) and a lower vector α_(j)X_(i)(k), representing the correlationcharacteristics of the horizontal and vertical antenna groups,respectively. X_(i)(k) is expressed as a vector having the linear phaseincrement property, reflecting the correlation characteristics betweenantennas in each antenna group. For example, a Discrete FourierTransform (DFT) matrix may be used for X_(i)(k).

4 Tx Dual Codebook Downscaled from 8 Tx Codebook

In an LTE Rel-10 system, an 8 Tx codebook for a BS having 8 Tx antennasis defined. The above codebook is a dual codebook structure in which twocodebooks are multiplied and includes W⁽¹⁾ codebook includingwideband/longterm channel information and W⁽²⁾ codebook includingsubband/shorter channel information. Recently, a codebook similar to the8Tx codebook defined in the LTE Rel-10 system was proposed as one of 4Txcodebook. The proposed codebook is as follows.

The overall precoder is formed as the product of W⁽¹⁾ and W⁽²⁾ accordingto [Equation 14] below.

W=W ⁽¹⁾ W ⁽²⁾  [Equation 14]

The inner precoder W⁽¹⁾ is then selected from a first codebook C⁽¹⁾according to [Equation 15] below.

$\begin{matrix}{{C^{\prime {(1)}} = \begin{Bmatrix}\left. \begin{bmatrix}{\overset{\sim}{W}}^{(1)} & 0 \\0 & {\overset{\sim}{W}}^{(1)}\end{bmatrix} \right| \\{{{\overset{\sim}{W}}^{(1)} = \begin{bmatrix}\begin{matrix}w_{2k\; {mod}\; 16} & w_{{({{2k}\; + 1})}{mod}\; 16}\end{matrix} \\\begin{matrix}w_{{({{2k} + 2})}\; {mod}\; 16} & w_{{({{2k} + 3})}\; {mod}\; 16}\end{matrix}\end{bmatrix}},} \\{{k = 0},1,\ldots \mspace{14mu},7}\end{Bmatrix}}{{{{where}\mspace{14mu} w_{n}} = \begin{bmatrix}1 \\e^{j\frac{2\pi \; n}{16}}\end{bmatrix}},{n = 0},1,\ldots \mspace{14mu},15}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

The outer precoder W⁽²⁾ for rank 1 transmission is selected from asecond codebook C₁ ⁽²⁾ according to [Equation 16] below.

$\begin{matrix}{{C_{1}^{(2)} = \left\{ {\begin{bmatrix}Y \\{a_{1}Y}\end{bmatrix},\begin{bmatrix}Y \\{{- a_{1}}Y}\end{bmatrix},\begin{bmatrix}Y \\{j\; a_{1}Y}\end{bmatrix},\begin{bmatrix}Y \\{{- j}\; a_{1}Y}\end{bmatrix}} \right\}}{Y \in \left\{ {e_{1},e_{2},e_{3},e_{4}} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

Here, e_(n) is a selection vector with all zeros except for an n^(th)element where n is 1 to 4. In addition, a_(n)=e^(jφ) ^(n) is satisfiedand φ_(n) is a phase value determined by a codeword index of C⁽¹⁾ and C₁⁽²⁾ and is responsible for compensation such that

$\quad\begin{bmatrix}Y \\{a_{1}Y}\end{bmatrix}$

has LPI property.

An outer precoder W⁽²⁾ for rank 2 transmission is selected from thesecond codebook C₂ ⁽²⁾.

$\begin{matrix}{{C_{2}^{(2)} = \left\{ {\begin{bmatrix}Y_{1} & Y_{2} \\{a_{1}Y} & {{- a_{2}}Y_{2}}\end{bmatrix},\begin{bmatrix}Y_{1} & Y_{2} \\{j\; a_{1}Y_{1}} & {{- j}\; a_{2}Y_{2}}\end{bmatrix}} \right\}}{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),} \\{\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)}\end{Bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

Here, e_(n) is a 4-element selection vector with all zeros except forthe n^(th) element. In addition, a_(n)=e^(jφ) ^(n) is satisfied andφ_(n) is a phase value determined by a codeword index of C⁽¹⁾ and C₂ ⁽²⁾and is responsible for compensation such that each vector of

$\quad\begin{bmatrix}Y_{1} & Y_{2} \\{a_{1}Y} & {{- a_{2}}Y_{2}}\end{bmatrix}$

has LPI property.

The rank 1 codeword of the 4Tx codebook is generated as follows. A 2×2DFT matrix is oversampled eightfold to generate a 2×16 DFT matrix. Whenone of 16 vectors is selected and the selected 2×1 vector is v, vrepeatedly concatenates to generate a 4×1 vector of [v v]^(T). Inconsideration of four phase compensation values {1, j, −1, −j} for phasecompensation of a vertical antenna group and a horizontal antenna groupof X-pol antennas, one of {[v a₁v]^(T), [v a₁*j*v]^(T), [v−a₁*v]^(T),[v−_(a1)*j*v]^(T)} is selected. If compensation is not performed usinga₁, only eight vectors among a total of 64 rank 1 vectors have LPIproperty. The lower vector is multiplied by a1 to perform compensationsuch that codeword of [v a₁v]^(T) always has LPI property. As a result,16 vectors among a total of 64 rank 1 vectors have LPI property. a₁ isdetermined by a function of codewords of C⁽¹⁾ and C₂ ⁽²⁾.

Channel Property of ULA Antenna

The channel property of the ULA antenna may be expressed by the propertyof a dominant eigen vector of a channel. In general, in a correlatedenvironment in which a gap between ULA antenna ports is narrow, thedominant eigen vector has LPI property. Since transmit antenna ports areseparated at the same interval, the signal of each port has regularreception delay. That is, there is a reception time difference of Δibetween a signal received from a first transmit antenna and a signalreceived from an i^(th) transmit antenna. The reception time differenceappears as a phase change of a channel such that there is a phasedifference of τi between the signal received from the first transmitantenna and the signal received from the i^(th) transmit antenna and thechannel indicates LPI property. Accordingly, in a codebook optimized inthe correlated environment in which the gap between ULA antenna ports isnarrow, each codeword needs to have LPI property.

First Embodiment

The First Embodiment of the Present Invention Relates to 4 Tx Codebookof Rank 2.

The aforementioned 4Tx codebook includes a first codebook C⁽¹⁾ having asize of 3 bits and a second codebook C⁽²⁾ having a size of 4 bits ateach ran and thus has a size of a total of 7 bits (here, the secondcodebook is defined to be divided into C₁ ⁽²⁾ and C₂ ⁽²⁾ according torank but, for convenience of description, the second codebook is C⁽²⁾irrespective of rank). Some of rank 1 codewords generated as thecodebook have the LPI property in consideration of the ULA antenna.However, a codeword having LPI property is not present in both first andsecond columns among the rank 2 codewords generated as the codebook.

Accordingly, in rank 2 or more, the codebook is requested such that allbeam vectors have LPI properties in order to improve a codebookperformance in a high correlated ULA antenna. In addition, in order tominimize inter-stream interference, it is necessary to generate thecodebook such that the beam vectors are orthonomal to each other.Hereinafter, a codebook having the following two properties in rank 2 ormore will be proposed. First, all beam vectors have LPI property.Second, all beam vectors need to be orthonomal to each other.

The present invention proposes a codeword in which all beam vectors haveLPI property and orthonomal property in rank 2 or more and proposes acodebook having a codeword having such a property. The 4 Tx codebook ofrank 2 includes only codewords having the above properties or codewordshaving the above properties.

The rank 2 codeword generated based on Equations 14 to 18 is representedaccording to [Equation 18] below

$\begin{matrix}{\quad{\begin{bmatrix}{w_{n}\mspace{14mu}} & w_{m} \\{{a_{1}w_{n}}\mspace{31mu}} & {{- a_{2}}w_{m}}\end{bmatrix},{{or}\mspace{14mu} {\quad\begin{bmatrix}w_{n} & w_{m} \\{j\; a_{1}w_{n}} & {{- j}\; a_{2}w_{m}}\end{bmatrix}}}}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack\end{matrix}$

Here, n and m refer to arbitrary DFT vector indices selected via C₂ ⁽²⁾and each of Wn and Wm refer one vector selected from the oversampled DFTvector

${w_{k} = \begin{bmatrix}1 \\e^{j\frac{2\pi \; k}{16}}\end{bmatrix}},{k = 0},1,\ldots \mspace{14mu},15.$

A condition of the following equation needs to be satisfied such thatall beam vectors of the rank 2 codeword of [Equation 18] have orthonomalproperty.

w _(n) ^(H) w _(m) −a ₁ ^(H) a ₂ w _(n) ^(H) w _(m)=0  [Equation 19]

In order to satisfy the above equation, a₁=a₂ or w_(n) ^(H)w_(m)=0 needsto be satisfied.

When the condition a₁=a₂ is satisfied such that all beam vectors haveorthonomal property, a condition required to satisfy LPI property willnow be described.

Under the assumption of a₁=a₂ e^(jφ), [Equation 18] is summarizedaccording to [Equation 20] below.

$\begin{matrix}{\begin{bmatrix}1 & 1 \\e^{j\frac{2\pi}{16}{(n)}} & e^{j\frac{2\pi}{16}{(m)}} \\e^{j\; \varphi} & {- e^{j\; \varphi}} \\e^{j{({\frac{2\pi}{16}{({n + \varphi})}})}} & {- e^{j{({\frac{2\pi}{16}{({m + \varphi})}})}}}\end{bmatrix},{{or}\; \text{}\begin{bmatrix}1 & 1 \\e^{j\frac{2\pi}{16}{(n)}} & e^{j\frac{2\pi}{16}{(m)}} \\{j\; e^{j\; \varphi}} & {{- j}\; e^{j\; \varphi}} \\{j\; e^{j{({\frac{2\pi}{16}{({n + \varphi})}})}}} & {{- j}\; e^{j{({\frac{2\pi}{16}{({m + \varphi})}})}}}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack\end{matrix}$

As shown in the left of [Equation 20] above, [Equation 21] needs to besatisfied such that both two vectors have LPI property.

$\begin{matrix}{\varphi = {{2\frac{2\pi}{16}(n)} = {{2\frac{2\pi}{16}(m)} + {\pi \pm {2\pi}}}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

m and n that satisfy [Equation 21] above satisfy n=m±4.

However, if the existing codebook of [Equation 15] above is used, since|n−m|<4, it is impossible to generate a codeword having both orthonomalproperty and LPI property. Accordingly, in order to enable two vectorsconfiguring the rank 2 codeword to have the LPI property, C⁽¹⁾ and C₂⁽²⁾ need to be newly designed in the 4Tx codebook.

According to a first example of the 4 Tx codebook of rank 2, [Equation21] above is satisfied such that all vectors have LPI property andorthonomal property is satisfied according to a₁=a₂ among conditionsbased on [Equation 19] above.

C⁽¹⁾ and C₂ ⁽²⁾ according to the first example of the 4 Tx codebook ofrank 2 are configured according to [Equation 22] below.

$\begin{matrix}{C^{(1)} = \begin{Bmatrix}\left. \begin{bmatrix}{\overset{\sim}{W}}^{(1)} & 0 \\0 & {\overset{\sim}{W}}^{(1)}\end{bmatrix} \right| \\{{{\overset{\sim}{W}}^{(1)} = \begin{bmatrix}\begin{matrix}w_{4k\; {mod}\; 16} & w_{{({{4k}\; + 1})}{mod}\; 16} & w_{{({{4k} + 2})}\; {mod}\; 16}\end{matrix} \\\begin{matrix}{w_{{({{4k} + 3})}\; {mod}\; 16}\mspace{14mu} w_{{({{4k}\; + 4})}{mod}\; 16}} & w_{{({{4k} + 5})}\; {mod}\; 16}\end{matrix} \\\begin{matrix}w_{{({{4k} + 6})}\; {mod}\; 16} & w_{{({{4k} + 7})}\; {mod}\; 16}\end{matrix}\end{bmatrix}},} \\{{k = 0},1,2,3}\end{Bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

The inner precoder W⁽¹⁾ is selected from the first codebook C⁽¹⁾.

Here,

${w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\pi \; n}{16}}\end{bmatrix}},{n = 0},1,\ldots \mspace{14mu},15$

is satisfied and k is a codeword index of C⁽¹⁾. In addition, C⁽¹⁾(k) isa k^(th) codeword of the codebook C⁽¹⁾.

The outer precoder W⁽²⁾ for rank 2 transmission is selected from thesecond codebook C₂ ⁽²⁾ of [Equation 23] below.

$\begin{matrix}{\mspace{79mu} {{{C_{2}^{(2)} = \left\{ {\begin{bmatrix}Y_{1} & Y_{2} \\{a_{1}Y} & {{- a_{2}}Y_{2}}\end{bmatrix},\begin{bmatrix}Y_{1} & Y_{2} \\{j\; a_{1}Y_{1}} & {{- j}\; a_{2}Y_{2}}\end{bmatrix}} \right\}}\mspace{20mu} {\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},e_{5}} \right),\left( {e_{2},e_{6}} \right),\left( {e_{3},e_{7}} \right),\left( {e_{4},e_{8}} \right)} \right\}}}{C_{2}^{(2)} = {\left\{ \begin{matrix}{\begin{bmatrix}e_{1} & e_{5} \\{a_{1}e_{1}} & {{- a_{2}}e_{5}}\end{bmatrix},{\quad{\begin{bmatrix}e_{2} & e_{6} \\{a_{1}e_{2}} & {{- a_{2}}e_{6}}\end{bmatrix},\begin{bmatrix}e_{3} & e_{7} \\{a_{1}e_{3}} & {{- a_{2}}e_{7}}\end{bmatrix},}}} \\{\left\lbrack \begin{matrix}e_{4} & e_{8} \\{a_{1}e_{4}} & {{- a_{2}}e_{8}}\end{matrix} \right\rbrack,{\quad{\begin{bmatrix}e_{1} & e_{5} \\{j\; a_{1}e_{1}} & {{- j}\; a_{2}e_{5}}\end{bmatrix},\begin{bmatrix}e_{2} & e_{6} \\{j\; a_{1}e_{2}} & {{- j}\; a_{2}e_{6}}\end{bmatrix},}}} \\{\begin{bmatrix}e_{3} & e_{7} \\{j\; a_{1}e_{3}} & {{- j}\; a_{2}e_{7}}\end{bmatrix},\begin{bmatrix}e_{4} & e_{8} \\{j\; a_{1}e_{4}} & {{- j}\; a_{2}e_{8}}\end{bmatrix}}\end{matrix} \right\} \quad}}}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

Here, e_(n) is a 4-element selection vector with all zeros except forthe nth element. l is the codeword index of C₂ ⁽²⁾ and l=0, 1, 2, . . ., 7. In addition, C₂ ⁽²⁾(l) is an l^(th) codeword of the codebook C₂ ⁽²⁾and

$a_{1} = {a_{2} = e^{2{j{({\frac{2\; \pi}{16}{({{4k} + {l\; {mod}\; 4}})}\; {mod}\; 16})}}}}$

is satisfied.

C⁽¹⁾ according to the first example of the 4 Tx codebook of rank 2 isgenerated using the same oversampled DFT vector like C⁽¹⁾ of [Equation15] above.

However, distinguished from C⁽¹⁾ of [Equation 15] above, C⁽¹⁾ accordingto the first example of the 4 Tx codebook of rank 2 is composed of eightconsecutive oversampled DFT vectors in order to enable two beam vectorsconfiguring the rank 2 codeword to have the LPI property. Since C⁽¹⁾ of[Equation 15] above is composed of four consecutive oversampled DFTvectors, even if an arbitrary vector included in C⁽¹⁾ is selected usingC⁽²⁾, the two beam vectors which are finally generated do not have theLPI property. That is, in [Equation 21] above, |m−n|=4 is not satisfied.

Accordingly, C⁽¹⁾ according to the first example of the 4 Tx codebook ofrank 2 is composed of a fatter matrix and the type of the DFT vectorselected from C⁽¹⁾ via C⁽²⁾ is increased. That is, in [Equation 21]above, since 0<|m−n|<7, it may be possible to find m and n that satisfy|m−n|=4. As a result, the finally generated two beam vectors have LPIattribute.

A codeword having LPI property may be generated using C⁽¹⁾ and C⁽²⁾according to the first example of the 4 Tx codebook of rank 2. In C⁽²⁾,(Y₁,Y₂) is limited to (e_(i),e_(i+4)). As a result, in [Equation 21]above, |m−n|=4 is always satisfied. In addition, according to [Equation21] for enabling all beam vector configuring rank 2 to have theorthonomal property and the LPI property, in C₂ ⁽²⁾ according to thefirst example of the 4 Tx codebook of rank 2, a₁=a₂=e^(jφ), where

${\varphi = {2\left( {\frac{2\; \pi}{16}n} \right)}},$

n=(4k+l mod 4)mod 16 is set.

According to a second example of the 4 Tx codebook of rank 2, [Equation21]above is satisfied such that all vectors have LPI property andorthonomal property is satisfied according to a₁=a₂ among conditionsbased on [Equation 19] above.

C⁽¹⁾ and C₂ ⁽²⁾ according to the second example of the 4 Tx codebook ofrank 2 are configured according to [Equation 24] below.

                                    [Equation  24]$C^{(1)} = \begin{Bmatrix}{{\begin{bmatrix}{\overset{\sim}{W}}^{(1)} & 0 \\0 & {\overset{\sim}{W}}^{(1)}\end{bmatrix}{\overset{\sim}{W}}^{(1)}} =} \\{\quad {\left\lbrack \begin{matrix}w_{2k\; {mod}\; 8} & w_{{({{2k} + 1})}\; {mod}\; 8} & w_{{({{2k} + 2})}\; {mod}\; 8} & w_{{({{2k} + 3})}\; {mod}\; 8}\end{matrix} \right\rbrack,{k = 0},1,2,3}}\end{Bmatrix}$

The inner precoder W⁽¹⁾ is selected from the first codebook C⁽¹⁾.

Here,

${w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\; \pi \; n}{8}}\end{bmatrix}},{n = 0},1,\ldots \mspace{14mu},7$

is satisfied and k is a codeword index of C⁽¹⁾. In addition, C⁽¹⁾(k) isa k^(th) codeword of the codebook C⁽¹⁾.

The outer precoder W⁽²⁾ for rank 2 transmission is selected from thesecond codebook C₂ ⁽²⁾ of [Equation 25] below.

                                     [Equation  25]$\mspace{79mu} {C_{2}^{(2)} = \left\{ {\begin{bmatrix}Y_{1} & Y_{2} \\{a_{1}Y_{1}} & {{- a_{2}}Y_{2}}\end{bmatrix},\begin{bmatrix}Y_{1} & Y_{2} \\{{ja}_{1}Y_{1}} & {{- {ja}_{2}}Y_{2}}\end{bmatrix}} \right\}}$      (Y₁, Y₂) ∈ {(e₁, e₃), (e₂, e₄)}$C_{2}^{(2)} = \left\{ {\begin{bmatrix}e_{1} & e_{3} \\{a_{1}e_{1}} & {{- a_{2}}e_{3}}\end{bmatrix},\begin{bmatrix}e_{2} & e_{4} \\{a_{1}e_{2}} & {{- a_{2}}e_{4}}\end{bmatrix},\begin{bmatrix}e_{1} & e_{3} \\{{ja}_{1}e_{1}} & {{- {ja}_{2}}e_{3}}\end{bmatrix},\begin{bmatrix}e_{2} & e_{4} \\{{ja}_{1}e_{2}} & {{- {ja}_{2}}e_{4}}\end{bmatrix}} \right\}$

Here, e_(n) is a 4-element selection vector with all zeros except forthe nth element. l is the codeword index of C₂ ⁽²⁾ and l=0, 1, 2, 3. Inaddition, C₂ ⁽²⁾(l) is an l^(th) codeword of the codebook C₂ ⁽²⁾ and

$a_{1} = {a_{2} = e^{2{j{({\frac{2\; \pi}{16}{({{2k} + {l\; {mod}\; 2}})}\; {mod}\; 8})}}}}$

is satisfied.

C⁽¹⁾ according to the second example of the 4 Tx codebook of rank 2 iscomposed of a matrix having the same size as C⁽¹⁾ of [Equation 15]above.

However, distinguished from C⁽¹⁾ of [Equation 15] above, C⁽¹⁾ accordingto the second example of the 4 Tx codebook of rank 2 is composed of aDFT vector oversampled fourfold instead of eightfold in order to enabletwo beam vectors configuring the rank 2 codeword to have the LPIproperty. Since C⁽¹⁾ of [Equation 15] above is composed of a DFT vectoroversampled eightfold, even if an arbitrary vector included in C⁽¹⁾ isselected using C⁽²⁾, the two beam vectors which are finally generated donot have the LPI property.

Accordingly, C⁽¹⁾ according to the second example of the 4 Tx codebookof rank 2 may be composed of a DFT vector oversampled fourfold and twobeam vectors have LPI property via C⁽²⁾.

In the first example of the 4 Tx codebook of rank 2, C⁽²⁾ in order toenable the two beam vectors selected via C⁽²⁾ to have the LPI property,|m−n|=4 needs to be satisfied. However, the second example of the 4 Txcodebook of rank 2 corresponds to the case in which C⁽¹⁾ includes a DFTvector oversampled eightfold. Since C⁽¹⁾ according to the second exampleof the 4 Tx codebook of rank 2 is composed of a DFT vector oversampledfourfold, instead of |m−n|=4, |m−n|=2 needs to be satisfied. In order tosatisfy this condition, (Y₁,Y₂)ε{(e₁,e₃),(e₂, e₄)} is set in [Equation25] above. In addition, according to [Equation 21] for enabling all beamvectors configuring rank 2 to have the orthonomal property and the LPIproperty, C⁽¹⁾ according to the second example of the 4 Tx codebook ofrank 2 is set according to a₁=a₂=e^(jφ), where

${\varphi = {2\frac{2\; \pi}{16}(n)}},{n = {\left( {{2k} + {l\; {mod}\; 2}} \right)\; {mod}\; 8.}}$

According to a third example of the 4 Tx codebook of rank 2, [Equation21] above is satisfied such that all vectors have LPI property andorthonomal property is satisfied according to v_(n) ^(H)v_(m)=0 amongconditions based on [Equation 19] above.

In [Equation 19] above, when v_(n) ^(H)v_(m)=0 is satisfied, two beamvectors of rank 2 are always orthonomal with respect to arbitrary a₁,a₂. Accordingly, a codebook is designed to satisfy v_(n) ^(H)v_(m)=0and, when a₁, a₂ are calculated such that the beam vector correspondingto each rank has LPI property, a codebook having both orthonomalproperty and LPI property is generated.

The codebook according to the third example of the 4 Tx codebook of rank2 is configured according to [Equation 26] below.

                                    [Equation  26]$C^{(1)} = \begin{Bmatrix}{{\begin{bmatrix}{\overset{\sim}{W}}^{(1)} & 0 \\0 & {\overset{\sim}{W}}^{(1)}\end{bmatrix}{\overset{\sim}{W}}^{(1)}} =} \\{\quad {\left\lbrack \begin{matrix}w_{2k\; {mod}\; 16} & w_{{({{2k} + 1})}\; {mod}\; 16} & {w_{{({{2k} + 2})}\; {mod}\; 16}\mspace{20mu} \ldots} & w_{{({{2k} + 15})}\; {mod}\; 16}\end{matrix} \right\rbrack,{k = 0}}}\end{Bmatrix}$

The inner precoder W⁽¹⁾ is selected from the first codebook C⁽¹⁾.

Here,

${w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\; \pi \; n}{16}}\end{bmatrix}},{n = 0},1,\ldots \mspace{14mu},15$

is satisfied and k is a codeword index of C⁽¹⁾. In addition, C⁽¹⁾(k) isa k^(th) codeword of the codebook C⁽¹⁾.

The outer precoder W⁽²⁾ for rank 2 transmission is selected from thesecond codebook C₂ ⁽²⁾ according to [Equation 27] below.

                                     [Equation  27]$\mspace{79mu} {C_{2}^{(2)} = \left\{ {\begin{bmatrix}Y_{1} & Y_{2} \\{a_{1}Y_{1}} & {{- a_{2}}Y_{2}}\end{bmatrix},\begin{bmatrix}Y_{1} & Y_{2} \\{{ja}_{1}Y_{1}} & {{- {ja}_{2}}Y_{2}}\end{bmatrix}} \right\}}$$\mspace{79mu} {\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1},e_{9}} \right),\left( {e_{2},e_{10}} \right),\left( {e_{3},e_{11}} \right),\left( {e_{4},e_{12}} \right),} \\{\left( {e_{5},e_{13}} \right),\left( {e_{6},e_{14}} \right),\left( {e_{7},e_{15}} \right),\left( {e_{8},e_{16}} \right)}\end{Bmatrix}}$ $C_{2}^{(2)} = \begin{Bmatrix}{\begin{bmatrix}e_{1} & e_{9} \\{a_{1}e_{1}} & {{- a_{2}}e_{9}}\end{bmatrix},\begin{bmatrix}e_{2} & e_{10} \\{a_{1}e_{2}} & {{- a_{2}}e_{10}}\end{bmatrix},\begin{bmatrix}e_{3} & e_{11} \\{a_{1}e_{3}} & {a_{2}e_{11}}\end{bmatrix},\begin{bmatrix}e_{4} & e_{12} \\{a_{1}e_{4}} & {{- a_{2}}e_{12}}\end{bmatrix},} \\{\begin{bmatrix}e_{5} & e_{13} \\{a_{1}e_{5}} & {{- a_{2}}e_{13}}\end{bmatrix},\begin{bmatrix}e_{6} & e_{14} \\{a_{1}e_{6}} & {{- a_{2}}e_{14}}\end{bmatrix},\begin{bmatrix}e_{7} & e_{15} \\{a_{1}e_{7}} & {{- a_{2}}e_{15}}\end{bmatrix},\begin{bmatrix}e_{8} & e_{16} \\{a_{1}e_{8}} & {{- a_{2}}e_{16}}\end{bmatrix}} \\{\begin{bmatrix}e_{1} & e_{9} \\{{ja}_{1}e_{1}} & {{- {ja}_{2}}e_{9}}\end{bmatrix},\begin{bmatrix}e_{2} & e_{10} \\{{ja}_{1}e_{2}} & {{ja}_{2}e_{10}}\end{bmatrix},\begin{bmatrix}e_{3} & e_{11} \\{{ja}_{1}e_{3}} & {{- {ja}_{2}}e_{11}}\end{bmatrix},} \\{\begin{bmatrix}e_{4} & e_{12} \\{{ja}_{1}e_{4}} & {{- {ja}_{2}}e_{12}}\end{bmatrix},\begin{bmatrix}e_{5} & e_{13} \\{{ja}_{1}e_{5}} & {{- {ja}_{2}}e_{13}}\end{bmatrix},\begin{bmatrix}e_{6} & e_{14} \\{{ja}_{1}e_{6}} & {{- {ja}_{2}}e_{14}}\end{bmatrix},} \\{\begin{bmatrix}e_{7} & e_{15} \\{{ja}_{1}e_{7}} & {{- {ja}_{2}}e_{15}}\end{bmatrix},\begin{bmatrix}e_{8} & e_{16} \\{{ja}_{1}e_{i}} & {{- {ja}_{2}}e_{16}}\end{bmatrix}}\end{Bmatrix}$

Here, e_(n) is a 4-element selection vector with all zeros except forthe nth element. l is the codeword index of C₂ ⁽²⁾ and l=0, 1, 2, . . ., 15 is satisfied. In addition, C₂ ⁽²⁾(l) is an i^(th) codeword of thecodebook C₂ ⁽²⁾ and

${a_{1} = e^{2{j{({\frac{2\; \pi}{16}{({l\; {mod}\; 8})}})}}}},{a_{2} = e^{{2{j{({\frac{2\; \pi}{16}{({{({l\; {mod}\; 8})} + 8})}})}}} + {j\; \pi}}}$

is satisfied.

C⁽¹⁾ according to the third example of the 4 Tx codebook of rank 2 iscomposed of a DFT vector oversampled eightfold and has one codewordcomposed of all DFT vectors. v_(n) ^(H)v_(m)=0 in [Equation 19] issatisfied by restricting (Y₁,Y₂)={e_(i),e_(i+8)} of C₂ ⁽²⁾ according tothe third example of the 4 Tx codebook of rank 2. That is, in the rank 2codeword generated according to Equations 26 and 27, two beam vectorsare orthonomal and a₁ and a₂ are set according to [Equation 27] abovesuch that each beam vector has LPI property.

Although rank 2 is assumed in the aforementioned first to third examplesof the 4 Tx codebook of rank 2, the scope of the present invention isnot limited to rank 2 and includes an arbitrary codebook satisfying LPIproperty and orthonomal property using the aforementioned method at highrank such as rank 2 or more. In addition, the case in which some of therank 2 codebook described in the aforementioned embodiments issubsampled or an arbitrary codebook including the codebook is includedin the scope of the present invention.

Hereinafter, a case in which the aforementioned condition of the 4 Txcodebook of rank 2 is satisfied and the inner precoder W⁽¹⁾ and theouter precoder W⁽²⁾ are set to 4 bits and 1 bit, respectively will bedescribed.

First, W⁽¹⁾ may be set according to [Equation 28] below.

$\begin{matrix}{{{W_{1}(l)} = \begin{bmatrix}{{\overset{\sim}{W}}_{1}(l)} & 0 \\0 & {{{\overset{\sim}{W}}_{1}(l)}{D_{a}(l)}}\end{bmatrix}},{l \in \left\{ {0,1,2,\ldots \mspace{14mu},15} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack\end{matrix}$

Here, {tilde over (W)}₁(l) is set according to [Equation 29] below.

$\begin{matrix}{{{\overset{\sim}{W}}_{1}(l)} = {\quad{\begin{bmatrix}w_{{(l)}\; {mod}\; 16} & w_{{({l + 1})}\; {mod}\; 16} & \ldots & w_{{({l + 6})}\; {mod}\; 16} & w_{{({l + 7})}\; {mod}\; 16}\end{bmatrix},\mspace{79mu} {w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\; \pi \; n}{16}}\end{bmatrix}}}}} & \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack\end{matrix}$

In addition, according to [Equation 30] below, D_(a)(l) is composed of ap^(th) row and a q^(th) column, where p and q are started from 0.

$\begin{matrix}{\left\{ {D_{a}(l)} \right\}_{pq} = \left\{ {\begin{matrix}e^{{{2 \cdot j}\frac{{2\; {\pi \cdot {({({l + {p\; {mod}\; 4}})})}}\; {mod}\; 16})}{16}},} & {p = q} \\{0,} & {p \neq q}\end{matrix}.} \right.} & \left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack\end{matrix}$

W⁽²⁾ may be set according to the following equation.

${{W_{2}\left( {n_{1},n_{2}} \right)} = \begin{bmatrix}e_{n_{1}} & e_{n_{2}} \\e_{n_{1}} & {- e_{n_{2}}}\end{bmatrix}},{\left( {n_{1},n_{2}} \right) \in {\left\{ {\left( {1,5} \right),\left( {3,7} \right)} \right\} \mspace{14mu} {or}}}$${{W_{2}\left( {n_{1},n_{2}} \right)} = \begin{bmatrix}e_{n_{1}} & e_{n_{2}} \\e_{n_{1}} & {- e_{n_{2}}}\end{bmatrix}},{\left( {n_{1},n_{2}} \right) \in {\left\{ {\left( {1,5} \right),\left( {2,6} \right)} \right\}.}}$

Hereinafter, a case in which the aforementioned condition of the 4 Txcodebook of rank 2 is satisfied and the inner precoder W⁽¹⁾ and theouter precoder W⁽²⁾ are set to 3 bits and 2 bits, respectively will bedescribed.

First, W⁽¹⁾ may be set according to [Equation 31] below.

$\begin{matrix}{{{W_{1}(l)} = \begin{bmatrix}{{\overset{\sim}{W}}_{1}(l)} & 0 \\0 & {{{\overset{\sim}{W}}_{1}(l)}{D_{a}(l)}}\end{bmatrix}},{l \in \left\{ {0,1,2,\ldots \mspace{14mu},7} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack\end{matrix}$

Here, {tilde over (W)}₁(l) is set according to [Equation 32] below.

$\begin{matrix}{{{\overset{\sim}{W}}_{1}(l)} = {\quad{\left\lbrack \begin{matrix}w_{{({2l})}{mod}\; 16} & w_{{({{2l} + 1})}{mod}\; 16} & \ldots & w_{{({{2l} + 6})}{mod}\; 16} & w_{{({{2l} + 7})}{mod}\; 16}\end{matrix} \right\rbrack,\mspace{20mu} {w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\pi \; n}{16}}\end{bmatrix}}}}} & \left\lbrack {{Equation}\mspace{14mu} 32} \right\rbrack\end{matrix}$

In addition, according to the following equation, D_(a)(l) is composedof a p^(th) row and a q^(th) column, where p and q are started from 0.

$\begin{matrix}{\left\{ {D_{a}(l)} \right\}_{pq} = \left\{ {\begin{matrix}{e^{{2 \cdot j}\frac{2{\pi \cdot {({{({{2l} + {({p\; {mod}\; 4})}})}\; {mod}\; 16})}}}{16}},} & {p = q} \\{0,} & {p \neq q}\end{matrix}.} \right.} & \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack\end{matrix}$

W⁽²⁾ may be set according to the following equation.

${{W_{2}\left( {n_{1},n_{2}} \right)} = \begin{bmatrix}e_{n_{1}} & e_{n_{2}} \\e_{n_{1}} & {- e_{n_{2}}}\end{bmatrix}},{\left( {n_{1},n_{2}} \right) \in {\left\{ {\left( {1,5} \right),\left( {2,6} \right),\left( {3,7} \right),\left( {4,8} \right)} \right\}.}}$

Hereinafter, a case in which the aforementioned condition of the 4 Txcodebook of rank 2 is satisfied and the inner precoder W⁽¹⁾ and theouter precoder W⁽²⁾ are set to 3 bits and 1 bit, respectively will bedescribed.

First, W⁽¹⁾ may be set according to [Equation 34] below.

$\begin{matrix}{{{W_{1}(l)} = \begin{bmatrix}{{\overset{\sim}{W}}_{1}(l)} & 0 \\0 & {{{\overset{\sim}{W}}_{1}(l)}{D_{a}(l)}}\end{bmatrix}},{l \in \left\{ {0,1,2,\ldots \mspace{14mu},7} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 34} \right\rbrack\end{matrix}$

Here, {tilde over (W)}₁(l) is set according to [Equation 35] below.

$\begin{matrix}{{{\overset{\sim}{W}}_{1}(l)} = {\quad{\left\lbrack \begin{matrix}w_{{({2l})}{mod}\; 16} & w_{{({{2l} + 1})}{mod}\; 16} & \ldots & w_{{({{2l} + 6})}{mod}\; 16} & w_{{({{2l} + 7})}{mod}\; 16}\end{matrix} \right\rbrack,\mspace{20mu} {w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\pi \; n}{16}}\end{bmatrix}}}}} & \left\lbrack {{Equation}\mspace{14mu} 35} \right\rbrack\end{matrix}$

In addition, according to [Equation 36] below, D_(a)(l) is composed of ap^(th) row and a q^(th) column, where p and q are started from 0.

$\begin{matrix}{\left\{ {D_{a}(l)} \right\}_{pq} = \left\{ {\begin{matrix}{e^{{2 \cdot j}\frac{2{\pi \cdot {({{({{2l} + {({p\; {mod}\; 4})}})}\; {mod}\; 16})}}}{16}},} & {p = q} \\{0,} & {p \neq q}\end{matrix}.} \right.} & \left\lbrack {{Equation}\mspace{14mu} 36} \right\rbrack\end{matrix}$

W⁽²⁾ may be set according to the following equation.

${{W_{2}\left( {n_{1},n_{2}} \right)} = \begin{bmatrix}e_{n_{1}} & e_{n_{2}} \\e_{n_{1}} & {- e_{n_{2}}}\end{bmatrix}},{\left( {n_{1},n_{2}} \right) \in {\left\{ {\left( {1,5} \right),\left( {3,7} \right)} \right\} \mspace{14mu} {or}}}$${{W_{2}\left( {n_{1},n_{2}} \right)} = \begin{bmatrix}e_{n_{1}} & e_{n_{2}} \\e_{n_{1}} & {- e_{n_{2}}}\end{bmatrix}},{\left( {n_{1},n_{2}} \right) \in {\left\{ {\left( {1,5} \right),\left( {2,6} \right)} \right\}.}}$

Hereinafter, a case in which the aforementioned condition of the 4 Txcodebook of rank 2 is satisfied and the inner precoder W⁽¹⁾ and theouter precoder W⁽²⁾ are set to 4 bits and 2 bits, respectively.

First, W⁽¹⁾ is set according to [Equation 37] below.

$\begin{matrix}{{{W_{1}(l)} = \begin{bmatrix}{{\overset{\sim}{W}}_{1}(l)} & 0 \\0 & {{{\overset{\sim}{W}}_{1}(l)}{D_{a}(l)}}\end{bmatrix}},{l \in \left\{ {0,1,2,\ldots \mspace{14mu},15} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 37} \right\rbrack\end{matrix}$

Here, {tilde over (W)}₁(l) is set according to the following equation.

$\begin{matrix}{{{\overset{\sim}{W}}_{1}(l)} = {\quad{\left\lbrack \begin{matrix}w_{{(l)}{mod}\; 16} & w_{{({l + 1})}{mod}\; 16} & \ldots & w_{{({l + 6})}{mod}\; 16} & w_{{({l + 7})}{mod}\; 16}\end{matrix} \right\rbrack,\mspace{20mu} {w_{n} = \begin{bmatrix}1 \\e^{j\frac{2\pi \; n}{16}}\end{bmatrix}}}}} & \left\lbrack {{Equation}\mspace{14mu} 38} \right\rbrack\end{matrix}$

In addition, according to the following equation, D_(a)(l) is composedof a p^(th) row and a q^(th) column, where p and q are started from 0.

$\begin{matrix}{\left\{ {D_{a}(l)} \right\}_{pq} = \left\{ {\begin{matrix}{e^{{2 \cdot j}\frac{2{\pi \cdot {({{({l + {({p\; {mod}\; 4})}})}\; {mod}\; 16})}}}{16}},} & {p = q} \\{0,} & {p \neq q}\end{matrix}.} \right.} & \left\lbrack {{Equation}\mspace{14mu} 39} \right\rbrack\end{matrix}$

W⁽²⁾ may be set according to the following equation.

${{W_{2}\left( {n_{1},n_{2}} \right)} = \begin{bmatrix}e_{n_{1}} & e_{n_{2}} \\e_{n_{1}} & {- e_{n_{2}}}\end{bmatrix}},{\left( {n_{1},n_{2}} \right) \in {\left\{ {\left( {1,5} \right),\left( {2,6} \right),\left( {3,7} \right),\left( {4,8} \right)} \right\}.}}$

Second Embodiment

The Second Embodiment of the Present Invention Relates to 4 Tx Codebookof Rank 3 or 4.

4TX codebook of rank 3 or 4 according to the present invention may begenerated by sampling a 4 Tx codebook of LTE release 8 to reduce acodebook size. In general, in a high rank environment, systemperformance is not sensitive to a codebook size compared with a lowrank. For example, when a receiving end is not an IRC receiver,performance is not affected in a max rank even if any precoder is used.For this reason, a LTE 8 Tx codebook may be designed to remarkablyreduce a codebook size in a high rank, and in rank 8, a codebook size is0 bit. In consideration of this principle, hereinafter, a new code bookgenerated by sampling a LTE release-8 4 Tx codebook will be described.Accordingly, a codebook size may be reduced to save feedback overhead.

The LTE release-8 4 Tx codebook may be configured by selecting rank n ofcolumn vectors in each matrix of the following equation using apredetermined method.

For example, when rank is 4, 4 Tx codebook is as follows.

First, each matrix for a BPSK modulation method of 4 TX codebook of rank4 is as follows.

$\begin{matrix}{{W_{0} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}}{W_{2} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}}{W_{8} = {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}}}{W_{10} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}}}{W_{12} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & {- 1} \\1 & 1 & {- 1} & 1 \\1 & {- 1} & 1 & 1 \\{- 1} & 1 & 1 & 1\end{bmatrix}}}{W_{13} = {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & 1 \\1 & 1 & 1 & {- 1} \\{- 1} & 1 & 1 & 1 \\1 & {- 1} & 1 & 1\end{bmatrix}}}{W_{14} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & 1 \\{- 1} & 1 & 1 & 1 \\1 & 1 & 1 & {- 1} \\1 & 1 & {- 1} & 1\end{bmatrix}}}{W_{15} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & {- 1} \\{- 1} & 1 & {- 1} & {- 1} \\{- 1} & {- 1} & 1 & {- 1} \\{- 1} & {- 1} & {- 1} & 1\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 40} \right\rbrack\end{matrix}$

next, each matrix for a QPSK modulation method of 4 TX codebook of rank4 is as follows.

$\begin{matrix}{{W_{1} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}}{W_{3} = {\frac{1}{2}\begin{bmatrix}1 & j & {- 1} & {- j} \\{- j} & 1 & {- j} & 1 \\{- 1} & j & 1 & {- j} \\j & 1 & {j\;} & 1\end{bmatrix}}}{W_{9} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}}}{W_{11} = {\frac{1}{2}\begin{bmatrix}1 & j & 1 & j \\{- j} & 1 & j & {- 1} \\1 & {- j} & 1 & {- j} \\{- j} & {- 1} & j & 1\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 41} \right\rbrack\end{matrix}$

In addition, signs of imaginary numbers of each matrix of Equation 41above ma be changed according to the following equation.

$\begin{matrix}{{W_{1} = {\frac{1}{2}\begin{bmatrix}1 & j & {- 1} & {- j} \\{- j} & 1 & {- j} & 1 \\{- 1} & j & 1 & {- j} \\j & 1 & j & 1\end{bmatrix}}}{W_{3} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}}}{W_{9} = {\frac{1}{2}\begin{bmatrix}1 & j & 1 & j \\{- j} & 1 & j & {- 1} \\1 & {- j} & 1 & {- j} \\{- j} & {- 1} & j & 1\end{bmatrix}}}{W_{11} = {\frac{1}{2}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 42} \right\rbrack\end{matrix}$

Next, each matrix for an 8PSK modulation method of 4 TX codebook of rank4 is as follows.

$\begin{matrix}{{W_{4} = {\frac{1}{2}\begin{bmatrix}1 & \frac{1 - j}{\sqrt{2}} & {- j} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & 1 & \frac{{- 1} + j}{\sqrt{2}} & j \\j & \frac{{- 1} - j}{\sqrt{2}} & 1 & \frac{{- 1} + j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & {- j} & \frac{{- 1} - j}{\sqrt{2}} & 1\end{bmatrix}}}{W_{5} = {\frac{1}{2}\begin{bmatrix}1 & \frac{{- 1} - j}{\sqrt{2}} & j & \frac{1 - j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & 1 & \frac{1 + j}{\sqrt{2}} & {- j} \\{- j} & \frac{1 - j}{\sqrt{2}} & 1 & \frac{1 + j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & j & \frac{1 - j}{\sqrt{2}} & 1\end{bmatrix}}}{W_{7} = {\frac{1}{2}\begin{bmatrix}1 & \frac{1 + j}{\sqrt{2}} & j & \frac{{- 1} + j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & 1 & \frac{{- 1} - j}{\sqrt{2}} & {- j} \\{- j} & \frac{{- 1} + j}{\sqrt{2}} & 1 & \frac{{- 1} - j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & j & \frac{{- 1} + j}{\sqrt{2}} & 1\end{bmatrix}}}{W_{6} = {\frac{1}{2}\begin{bmatrix}1 & \frac{{- 1} + j}{\sqrt{2}} & {- j} & \frac{1 + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & 1 & \frac{1 - j}{\sqrt{2}} & j \\j & \frac{1 + j}{\sqrt{2}} & 1 & \frac{1 - j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & {- j} & \frac{1 + j}{\sqrt{2}} & 1\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 43} \right\rbrack\end{matrix}$

In addition, signs of imaginary numbers of each matrix of Equation 43above may be changed according to the following equation.

$W_{4} = {\frac{1}{2}\begin{bmatrix}1 & \frac{1 + j}{\sqrt{2}} & j & \frac{{- 1} + j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & 1 & \frac{{- 1} - j}{\sqrt{2}} & {- j} \\{- j} & \frac{{- 1} + j}{\sqrt{2}} & 1 & \frac{{- 1} - j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & j & \frac{{- 1} + j}{\sqrt{2}} & 1\end{bmatrix}}$ $W_{5} = {\frac{1}{2}\begin{bmatrix}1 & \frac{{- 1} + j}{\sqrt{2}} & {- j} & \frac{1 + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & 1 & \frac{1 - j}{\sqrt{2}} & j \\j & \frac{1 + j}{\sqrt{2}} & 1 & \frac{1 - j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & {- j} & \frac{1 + j}{\sqrt{2}} & 1\end{bmatrix}}$ $W_{7} = {\frac{1}{2}\begin{bmatrix}1 & \frac{1 - j}{\sqrt{2}} & {- j} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & 1 & \frac{{- 1} + j}{\sqrt{2}} & j \\j & \frac{{- 1} - j}{\sqrt{2}} & 1 & \frac{{- 1} + j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & {- j} & \frac{{- 1} - j}{\sqrt{2}} & 1\end{bmatrix}}$ $W_{6} = {\frac{1}{2}\begin{bmatrix}1 & \frac{{- 1} - j}{\sqrt{2}} & j & \frac{1 - j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & 1 & \frac{1 + j}{\sqrt{2}} & {- j} \\{- j} & \frac{1 - j}{\sqrt{2}} & 1 & \frac{1 + j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & j & \frac{1 - j}{\sqrt{2}} & 1\end{bmatrix}}$

As another example, when a rank is 3, three column vectors may beselected in the aforementioned 4 TX codebook of rank 4 using apredetermined method and 1/?? instead of ½ of a front part of a matrixmay be multiplied for normalization. In detail, when a rank is 3, the 4TX codebook is as follows.

First, each matrix for a BPSK modulation method of 4 TX codebook of rank3 is as follows.

$\begin{matrix}{{W_{0} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & 1 \\1 & 1 & {- 1} \\1 & {- 1} & {- 1} \\1 & {- 1} & 1\end{bmatrix}}}{W_{2} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & 1 \\{- 1} & 1 & 1 \\1 & 1 & 1 \\{- 1} & {- 1} & 1\end{bmatrix}}}{W_{8} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & {- 1} \\1 & 1 & 1 \\{- 1} & 1 & {- 1} \\{- 1} & 1 & 1\end{bmatrix}}}{W_{10} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & {- 1} \\{- 1} & 1 & {- 1} \\{- 1} & {- 1} & 1 \\1 & 1 & 1\end{bmatrix}}}{W_{12} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & 1 \\1 & 1 & {- 1} \\1 & {- 1} & 1 \\{- 1} & 1 & 1\end{bmatrix}}}{W_{13} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & {- 1} \\1 & 1 & 1 \\{- 1} & 1 & 1 \\1 & {- 1} & 1\end{bmatrix}}}{W_{14} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & 1 \\{- 1} & 1 & 1 \\1 & 1 & 1 \\1 & 1 & {- 1}\end{bmatrix}}}{W_{15} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & {- 1} \\{- 1} & 1 & {- 1} \\{- 1} & {- 1} & 1 \\{- 1} & {- 1} & {- 1}\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 44} \right\rbrack\end{matrix}$

Next, each matrix for a QPSK modulation method of 4 TX codebook of rank3 is as follows.

$\begin{matrix}{{W_{1} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- j} & {- 1} \\j & 1 & j \\{- 1} & {- j} & 1 \\{- j} & 1 & {- j}\end{bmatrix}}}{W_{3} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & j & {- 1} \\{- j} & 1 & {- j} \\{- 1} & j & 1 \\j & 1 & j\end{bmatrix}}}{W_{9} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & {- j} \\j & {- j} & {- 1} \\1 & 1 & j \\j & {- j} & 1\end{bmatrix}}}{W_{11} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & j \\{- j} & j & {- 1} \\1 & 1 & {- j} \\{- j} & j & 1\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 45} \right\rbrack\end{matrix}$

Next, each matrix for an 8PSK modulation method of 4 TX codebook of rank3 is as follows.

$\begin{matrix}{{W_{4} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & \frac{1 - j}{\sqrt{2}} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & 1 & j \\j & \frac{{- 1} - j}{\sqrt{2}} & \frac{{- 1} + j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & {- j} & 1\end{bmatrix}}}{W_{5} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & \frac{{- 1} - j}{\sqrt{2}} & \frac{1 - j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & 1 & {- j} \\{- j} & \frac{1 - j}{\sqrt{2}} & \frac{1 + j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & j & 1\end{bmatrix}}}{W_{7} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & j & \frac{{- 1} + j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & \frac{{- 1} - j}{\sqrt{2}} & {- j} \\{- j} & 1 & \frac{{- 1} - j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & \frac{{- 1} + j}{\sqrt{2}} & 1\end{bmatrix}}}{W_{6} = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- j} & \frac{1 + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & \frac{1 - j}{\sqrt{2}} & j \\j & 1 & \frac{1 - j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & \frac{1 + j}{\sqrt{2}} & 1\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 46} \right\rbrack\end{matrix}$

As a first principle for sampling 4Tx codebook of rank 3 or 4, analphabet constituting each codeword is considered. A matrix for the BPSKmodulation method has only a real number, but a QPSK or 8PSK matrix alsohas an imaginary number. When a UE is embodied, since computational loadis increased due to the imaginary values, it is advantageous to design acodebook configured with values of the BPSK matrix.

As a second principle for sampling a codebook, channel properties in ahigh rank is considered. Since X-pol and ULA antennas have differentchannel properties, it is optimum to use different codebooks dedicatedto the respective antenna configurations. However, as described above,since performance is not affected by a codebook in a high rank comparedwith a low rank, one codebook may be used in terms of complexity.

As a third principle for sampling codebook, the channel property of theX-pol antenna is considered. A codebook for generation of one codebookthat is appropriately operated in both X-pol and ULA need toappropriately reflect the channel properties of both antennaconfigurations. As described above, in terms of ULA, a column vectorindicating each beam may have linear phase increase attributes. However,in ULA with a narrow antenna interval, the probability that a high rankoccurs is reduced, and in ULA with a wide antenna interval, theprobability that a singular vector of a channel does not have linearphase increase attributes is high, and thus it is not appropriate tomaintain the linear phase increase attributes of a codebook in a highrank. Accordingly, it may be appropriate to design a more optimumcodebook compared with the X-pol channel. As described above, the X-polchannel is configured such a way that channels of a horizontal antennaand a vertical antenna have the same value and a phase differencebetween the two antennas is present. Accordingly, in a release-8codebook, it may be appropriate to select a codebook with thisconfiguration maintained.

In consideration of the three above principles, hereinafter, a codebookfor rank 3 or 4 configured with 1 bit, 2 bits, or 3 bits is proposed.

First, the codebook for rank 3 or 4 configured with 1 bit may beconfigured as follows.

The 1-bit codebook may be configured with only W₀ and W₂ in Equation 40.Release-8 method may be applied to permutation of a column vector andselection of a column vector for each rank without changes.

The 1-bit codebook is configured with BPSK values according to the firstprinciple and is commonly applied to all antenna configurationsaccording to the second principle, and satisfies a channel configurationof the X-pol according to the third principle.

Next, a codebook for rank 3 or 4 of 2 bits may be configured as follows.

The 2-bit codebook according to the present invention may be configuredwith only W₀, W₂, W₈, and W₁₀ in Equations 40 to 46.

For example, a codebook index of 0, 2, 8, and 10 may be induced byapplying a second PMI index I_(PMI2) having one of 0 to 3 to thefollowing equation.

2I _(PMI2)+4·└I _(PMI2)/2┘  [Equation 47]

As described above, the release-8 method may be applied to permutationof a column vector and selection of a column vector for each rankwithout changes.

The 2-bit codebook is configured with BPSK values according to the firstprinciple and is commonly applied to all antenna configurationsaccording to the second principle, and satisfies a channel configurationof the X-pol according to the third principle.

As another example, the 2-bit codebook for rank 3 or 4 may be configuredwith only W₁, W₃, W₉, and W₁₁ in Equations 40 to 46. The release-8method may be applied to permutation of a column vector and selection ofa column vector for each rank without changes. The codebook isconfigured with the aforementioned QPSK values, is commonly applied toall antenna configurations according to the second principle, andsatisfies a channel configuration of the X-pol according to the thirdprinciple.

As another example, the 2-bit codebook for rank 3 or 4 may be configuredwith only W₄, W₅, W₆, and W₇ in Equations 40 to 46. The release-8 methodmay be applied to permutation of a column vector and selection of acolumn vector for each rank without changes. The codebook is configuredwith 8PSK values, is commonly applied to all antenna configurationsaccording to the second principle, and satisfies a channel configurationof the X-pol according to the third principle.

Next, a codebook for rank 3 or 4 of 3 bits may be configured as follows.

The 3-bit codebook may be configured with only W₀, W₂, W₈, W₁₀, W₁₂,W₁₃, W₁₄, and W₁₅ in Equations 40 to 46. The release-8 method may beapplied to permutation of a column vector and selection of a columnvector for each rank without changes.

The 3-bit codebook is configured with BPSK values according to the firstprinciple and is commonly applied to all antenna configurationsaccording to the second principle. However, W₁₂, W₁₃, W₁₄, and W₁₅ donot satisfy the channel configuration of the X-pol, and thus the thirdprinciple is not satisfied.

As another example, a 3-bit codebook may be configured with only W₀, W₂,W₈, W₁₀, W₁, W₃, W₉, and W₁₁ in Equations 40 to 46. The release-8 methodmay be applied to permutation of a column vector and selection of acolumn vector for each rank without changes. The codebook does notsatisfy the first principle. However, the codebook is commonly appliedto all antenna configurations according to the second principle andsatisfies the channel configuration of the X-pol according to the thirdprinciple.

As another example, a 3-bit codebook may be configured with only W₀, W₂,W₈, W₁₀, W₄, W₅, W₆, and W₇ in Equations 40 to 46. The release-8 methodmay be applied to permutation of a column vector and selection of acolumn vector for each rank without changes. The codebook does notsatisfy the first principle. However, the codebook is commonly appliedto all antenna configurations according to the second principle andsatisfy the channel configuration of the X-pol.

Next, as a 0-bit codebook, although rank 3 uses the aforementionedcodebook, a codebook may not be formed with respect to rank 4. That is,the rank 4 codebook is fixed to a 4 by 4 identity matrix.

Third Embodiment

The Third Embodiment of the Present Invention Relates to a CodebookSubsampling Method According to a PUCCH Feedback Mode in the Case ofRank 3 or 4.

LTE release-12 has discussed introduction of an enhanced 4 Tx codebookcompared with a legacy codebook. Hereinafter, the present inventionproposes codebook subsampling of PUCCH feedback modes 1-1 and 2-1 when anew codebook having W₁ and W₂ dual codebook structures is introducedwith respect to ranks 1 and 2 and a legacy release-8 codebook is usedwith respect to ranks 3 and 4.

First, the PUCCH feedback mode 1-1 includes submodes A and B when thedual codebook structure is used.

FIG. 15 is a diagram illustrating an example of the submode A of thePUCCH feedback mode 1-1.

Referring to FIG. 15, wideband W2 and wideband CQI are set to offset 1and periodicity 2 and RI and W1 are set to offset 0 and periodicity 16.

In the 8Tx codebook, as shown in Table 1 below, RI and W1 arejoint-encoded in 5 bits and in this case, and W1 is subsampled asfollows in order to reduce the sizes of payloads of RI and W1 to reportinformation with a low coding rate. Since RI is referred to by theremaining PMI and CQI, encoding needs to be performed with a low codingrate in order to prevent a decoding error in RI from occurring.

TABLE 1 hypotheses RI values 0-7 1 {0, 2, 4, 6, 8, 10, 12, 14}  8-15 2{0, 2, 4, 6, 8, 10, 12, 14} 16-17 3 {0, 2} 18-19 4 {0, 2} 20-21 5 {0, 2}22-23 6 {0, 2} 24-25 7 {0, 2} 26 8 {0} 27-31 reserved NA

When LTEA release-12 introduces a 4Tx dual codebook with respect toranks 1 and 2 and uses a legacy release-8 4Tx codebook with respect toranks 3 and 4, the subsampled W1 and RI may be joint-encoded to beencoded in 5 bits or less, similarly to the case of 8Tx. For example, acodebook may be subsampled in 3 bits with respect to ranks 3 and 4according to one of Tables 2 to 4 below.

TABLE 2 hypotheses RI W1 values 0 − k 1 To Be Determined (k + 1) − n    2 To Be Determined (n + 1) − (n + 8) 3 {0, 2, 8, 10, 12, 13, 14, 15} (n + 9) − (n + 16) 4 {0, 2, 8, 10, 12, 13, 14, 15}

TABLE 3 hypotheses RI W1 values 0 − k 1 To Be Determined (k + 1) − n    2 To Be Determined (n + 1) − (n + 8) 3 {0, 2, 8, 10, 1, 3, 9, 11}  (n +9) − (n + 16) 4 {0, 2, 8, 10, 1, 3, 9, 11}

TABLE 4 hypotheses RI W1 values 0 − k 1 To Be Determined (k + 1) − n    2 To Be Determined (n + 1) − (n + 8) 3 {0, 2, 8, 10, 4, 5, 6, 7}  (n +9) − (n + 16) 4 {0, 2, 8, 10, 4, 5, 6, 7}

One of Tables 2 to 4 above may be configured via a subsampling methodwith respect to ranks 3 and 4. That is, a 3-bit codebook that issubsampled from a release-8 codebook according to the aforementionedprinciple for subsampling a codebook may be applied to PUCCH feedbackmode 1-1 in the same way.

In Mode 1-1, W2 of ranks 3 and 4 is not transmitted. That is, only W1 ispresent as PMI with respect to ranks 3 and 4. In Tables 2 to 4 above,“To Be Determined” of ranks 1 and 2 may be determined as {0, 2, 4, 6, 8,10, 12, 14} like in the case of 8Tx, and in this case, k and n are 7 and15, respectively.

When a dual codebook structure is used, PUCCH feedback mode 2-1 may bedefined via two methods according to a PTI value. FIG. 16 illustratesPUCCH feedback mode 2-1 according to a PTI value. A wideband W1 ispresent with periodicity of 8 subframes in PUCCH feedback resource withoffset 1 and periodicity 2 and a wideband W2 and CQI are present in theremaining resource. RI and PTI are set with periodicity 16 and offset 0.When PTI is set to 1, L-bit information indicating subband W2 andsubband CQI, and a subband index is reported as shown in FIG. 16.

When the L-bit information indicating subband W2 and subband CQI, and asubband index is reported in a 8Tx codebook, W2 is subsampled as shownin Table 5 below. Information may be transmitted in 11 bits as a size ofa payload of PUCCH format 2 through the subsampling method.

TABLE 5 Relationship between the second PMI value and codebook index i₂Value of the second PMI RI I_(PMI2) Codebook index i₂ 1  0-15  I_(PMI2)2 0-3 2I_(PMI2) 3 0-3 8 · └I_(PMI2)/2┘ + (I_(PMI2) mod 2) + 2 4 0-32I_(PMI2) 5 0 0 6 0 0 7 0 0 8 0 0

When LTEA release-12 introduces a 4Tx dual codebook with respect toranks 1 and 2 and uses a legacy release-8 4Tx codebook with respect toranks 3 and 4, W2 needs to be subsampled similarly to the case of 8Tx soas not to exceed the size of a payload of PUCCH format 2. With respectto ranks 3 and 4, CQI is 7 bits and L is a maximum of 2 bits, and thusW2 is subsampled in 2 bits as follows. That is, subsampling may beperformed with respect to ranks 3 and 4 according to one of Tables 6 to8 below.

TABLE 6 RI W2 values 1 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} 2 To Be Determined 3 {0, 2, 8, 10} 4 {0, 2, 8, 10}

TABLE 7 RI W2 values 1 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} 2 To Be Determined 3 {1, 3, 9, 11} 4 {1, 3, 9, 11}

TABLE 8 RI W2 values 1 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} 2 To Be Determined 3 {4, 5, 6, 7} 4 {4, 5, 6, 7}

One of Tables 6 to 8 above may be configured via a subsampling methodwith respect to ranks 3 and 4. That is, a 2-bit codebook that issubsampled from a release-8 codebook according to the aforementionedprinciple for subsampling a codebook may be applied to PUCCH feedbackmode 2-1 in the same way.

In Mode 2-1, W1 of ranks 3 and 4 is not transmitted. That is, only W2 ispresent as PMI with respect to ranks 3 and 4. In Tables 6 to 8 above,“To Be Determined” of rank 2 may be determined as {0, 2, 4, 6, 8, 10,12, 14} like in the case of 8Tx, and in this case, n is 23.

Fourth Embodiment

A fourth embodiment of the present invention relates to a codebooksubsampling method when a new codebook having W₁ and W₂ dual codebookstructures with respect to ranks 1 and 2 are introduced.

First, codebook W₁ for ranks 1 and 2 may be set as follows.

$\begin{matrix}{\mspace{79mu} {{{W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n = 0},1,\ldots \mspace{14mu},15}{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{{(n)}{mod}\; 16} & q_{1}^{{({n + 1})}{mod}\; 16} & q_{1}^{{({n + 2})}{mod}\; 16} & q_{1}^{{({n + 3})}{mod}\; 16}\end{bmatrix}}\mspace{20mu} {q_{1} = {\exp \left( {j\; 2\; {\pi/16}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 48} \right\rbrack\end{matrix}$

Then codebook W₂ for ranks 1 and 2 may be set as follows.

$\begin{matrix}{{{W_{2} \in C_{2}} = \left\{ {\begin{bmatrix}Y \\Y\end{bmatrix},\begin{bmatrix}Y \\{j\; Y}\end{bmatrix},\begin{bmatrix}Y \\{- Y}\end{bmatrix},\begin{bmatrix}Y \\{{- j}\; Y}\end{bmatrix}} \right\}}{Y \in \left\{ {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{3},{\overset{\sim}{e}}_{4}} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 49} \right\rbrack\end{matrix}$

Here, {tilde over (e)}_(n) is a 4×1 selection vector with all zerosexcept for the n^(th) element with 1.

That is, C₂ for rank 1 includes 16 vectors according to the followingequation below and a codeword index is conformable to an order of thefollowing equation. That is, in the following equation, a first vectorhas an index 0 and is indexed in an ascending order.

                                     [Equation  50]$C_{2} = \left\{ \begin{matrix}{\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{j{\overset{\sim}{e}}_{1}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{- {\overset{\sim}{e}}_{1}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{{- j}{\overset{\sim}{e}}_{1}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{j{\overset{\sim}{e}}_{2}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{- {\overset{\sim}{e}}_{2}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{{- j}{\overset{\sim}{e}}_{2}}\end{bmatrix},} \\{\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{j{\overset{\sim}{e}}_{3}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{- {\overset{\sim}{e}}_{3}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{{- j}{\overset{\sim}{e}}_{3}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{j{\overset{\sim}{e}}_{4}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{- {\overset{\sim}{e}}_{4}}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{{- j}{\overset{\sim}{e}}_{4}}\end{bmatrix}}\end{matrix} \right\}$$\mspace{20mu} {{W_{2} \in C_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{j\; Y_{1}} & {{- j}\; Y_{2}}\end{bmatrix}}} \right\}}$$\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{1}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{2}} \right),\left( {{\overset{\sim}{e}}_{3},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{4},{\overset{\sim}{e}}_{4}} \right),\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{2}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{3}} \right),\left( {{\overset{\sim}{e}}_{1},{\overset{\sim}{e}}_{4}} \right),\left( {{\overset{\sim}{e}}_{2},{\overset{\sim}{e}}_{4}} \right)} \right\}$

That is, C₂ for rank 2 includes 16 vectors according to the followingtable and a codeword index is conformable to an order of the followingtable. That is, in the following table, a first vector has index 0 andis indexed in an ascending order.

TABLE 9 W2 index of rank 2  0 $\begin{bmatrix}{\overset{\sim}{e}}_{1} & {{\overset{\sim}{e}}_{1}\mspace{14mu}} \\{\overset{\sim}{e}}_{1} & {- {\overset{\sim}{e}}_{1}}\end{bmatrix}\quad$  1 $\begin{bmatrix}{\overset{\sim}{e}}_{1} & {{\overset{\sim}{e}}_{1}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{1}} & {{- j}{\overset{\sim}{e}}_{1}}\end{bmatrix}\quad$  2 $\begin{bmatrix}{\overset{\sim}{e}}_{2} & {{\overset{\sim}{e}}_{2}\mspace{14mu}} \\{\overset{\sim}{e}}_{2} & {- {\overset{\sim}{e}}_{2}}\end{bmatrix}\quad$  3 $\begin{bmatrix}{\overset{\sim}{e}}_{2} & {{\overset{\sim}{e}}_{2}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{2}} & {{- j}{\overset{\sim}{e}}_{2}}\end{bmatrix}\quad$  4 $\begin{bmatrix}{\overset{\sim}{e}}_{3} & {{\overset{\sim}{e}}_{3}\mspace{14mu}} \\{\overset{\sim}{e}}_{3} & {- {\overset{\sim}{e}}_{3}}\end{bmatrix}\quad$  5 $\begin{bmatrix}{\overset{\sim}{e}}_{3} & {{\overset{\sim}{e}}_{3}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{3}} & {{- j}{\overset{\sim}{e}}_{3}}\end{bmatrix}\quad$  6 $\begin{bmatrix}{\overset{\sim}{e}}_{4} & {{\overset{\sim}{e}}_{4}\mspace{14mu}} \\{\overset{\sim}{e}}_{4} & {- {\overset{\sim}{e}}_{4}}\end{bmatrix}\quad$  7 $\begin{bmatrix}{\overset{\sim}{e}}_{4} & {{\overset{\sim}{e}}_{4}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{4}} & {{- j}{\overset{\sim}{e}}_{4}}\end{bmatrix}\quad$  8 $\begin{bmatrix}{\overset{\sim}{e}}_{1} & {{\overset{\sim}{e}}_{2}\mspace{14mu}} \\{\overset{\sim}{e}}_{1} & {- {\overset{\sim}{e}}_{2}}\end{bmatrix}\quad$  9 $\begin{bmatrix}{\overset{\sim}{e}}_{1} & {{\overset{\sim}{e}}_{2}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{1}} & {{- j}{\overset{\sim}{e}}_{2}}\end{bmatrix}\quad$ 10 $\begin{bmatrix}{\overset{\sim}{e}}_{2} & {{\overset{\sim}{e}}_{3}\mspace{14mu}} \\{\overset{\sim}{e}}_{2} & {- {\overset{\sim}{e}}_{3}}\end{bmatrix}\quad$ 11 $\begin{bmatrix}{\overset{\sim}{e}}_{2} & {{\overset{\sim}{e}}_{3}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{2}} & {{- j}{\overset{\sim}{e}}_{3}}\end{bmatrix}\quad$ 12 $\begin{bmatrix}{\overset{\sim}{e}}_{1} & {{\overset{\sim}{e}}_{4}\mspace{14mu}} \\{\overset{\sim}{e}}_{1} & {- {\overset{\sim}{e}}_{4}}\end{bmatrix}\quad$ 13 $\begin{bmatrix}{\overset{\sim}{e}}_{1} & {{\overset{\sim}{e}}_{4}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{1}} & {{- j}{\overset{\sim}{e}}_{4}}\end{bmatrix}\quad$ 14 $\begin{bmatrix}{\overset{\sim}{e}}_{2} & {{\overset{\sim}{e}}_{4}\mspace{14mu}} \\{\overset{\sim}{e}}_{2} & {- {\overset{\sim}{e}}_{4}}\end{bmatrix}\quad$ 15 $\begin{bmatrix}{\overset{\sim}{e}}_{2} & {{\overset{\sim}{e}}_{4}\mspace{14mu}} \\{j{\overset{\sim}{e}}_{2}} & {{- j}{\overset{\sim}{e}}_{4}}\end{bmatrix}\quad$

When PUCCH feedback mode 1-1 uses a dual codebook structure, submodes Aand B are present. FIG. 17 illustrates a submode B when the new codebookis applied.

Referring to FIG. 17, wideband W1/W2 and wideband CQI are set to offset1 and periodicity 2 and RI and W1 are set to offset 0 and periodicity16.

In the 8Tx codebook, as shown in Table 10 below, W1 and W2 aresubsampled to wideband W1/W2 and wideband CQI.

TABLE 10 PMI for W1 PMI for W2 total RI #bits values #bits values #bits1 3 {0, 2, 4, 6, 8, 1 {0, 2} 4 10, 12, 14}, 2 3 {0, 2, 4, 6, 8, 1 {0, 1}4 10, 12, 14} 3 1 {0, 2} 3 {0, 1, 2, 3, 8, 4 9, 10, 11} 4 1 {0, 1} 3 {0,1, 2, 3, 4 4, 5, 6, 7} 5 2 {0, 1, 2, 3} 0 {0} 2 6 2 {0, 1, 2, 3} 0 {0} 27 2 {0, 1, 2, 3} 0 {0} 2 8 0 {0} 0 {0} 0

8Tx W1 of ranks 1 and 2 is defined as shown in the following equation.That is, i^(th) PMI and (i+1)^(th) PMI share two overlapped DFT vectors.As such, two DFT vectors may be overlapped between adjacent PMIs so asto more accurately feedback a channel. However, in consideration of alimited PUCCH resource, PMI of even-numbered W1 may be limited to aneven number so as to be subsumed. Overlapped DFT vectors are not presentbetween even-numbered PMIs but a UE can still represent a total of 32DFT vectors using W1 so as to minimize performance degradation.

$\begin{matrix}{\mspace{79mu} {{{B = \begin{bmatrix}b_{0} & b_{1} & \ldots & b_{31}\end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = e^{j\frac{2{\pi {mn}}}{32}}},\mspace{20mu} {m = 0},1,2,3,\; {n = 0},1,\ldots \mspace{14mu},31}{X^{(k)} \in \left\{ {{{\begin{bmatrix}b_{2k\; {mod}\; 32} & b_{{({{2k} + 1})}\; {mod}\; 32} & b_{{({{2k} + 2})}{mod}\; 32} & b_{{({{2k} + 3})}{mod}\; 32}\end{bmatrix}\text{:}\mspace{14mu} k} = 0},1,\ldots \mspace{14mu},15} \right\}}\mspace{20mu} {W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}}\mspace{20mu} {{{Codebook}\mspace{14mu} 1\text{:}\mspace{20mu} C_{1}} = \left\{ {W_{1}^{(0)},W_{1}^{(1)}\;,W_{1}^{(2)},\ldots \mspace{14mu},W_{1}^{(15)}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 50} \right\rbrack\end{matrix}$

Similarly to 8 Tx codebook subsampling, a new 4Tx codebook also requiressubsampling and may be subsampled with respect to ranks 1 and 2 as shownin the following table.

TABLE 11 PMI for W1 PMI for W2 total RI #bits values #bits values #bits1 2 {0, 4, 8, 12} 2 {0, 2, k1, k2} 4 2 2 {0, 4, 8, 12} 2 {k3, k4, k5,k6} 4

First, W1 subsampling of 4 Tx codebook will be described below.

W1 subsampling of 4 Tx codebook may be performed similarly to W1subsampling in 8Tx codebook. In the above table, with regard to W1,i^(th) PMI and (i+1)^(th) PMI share three overlapped DFT vectors. Inaddition, i^(th) PMI and (i+2)^(th) PMI share two overlapped DFT vectorsand i^(th) PMI and (i+3)^(th) PMI share one overlapped DFT vector.

That is, in consideration of a limited PUCCH resource, PMI of W1 exceptfor overlapped PMI may be subsampled to {0, 4, 8, 12}. Overlapped DFTvectors are not present between the subsampled PMIs, a UE can stillrepresent a total of 16 DFT vectors using W1 so as to minimizeperformance degradation.

Next, W2 subsampling of 4 Tx codebook in the case of rank 1 will bedescribed below.

In the case of rank 1, W2 subsampling of 4 Tx codebook may be embodiedin various ways according to configurations of indexes k1, k2, k3, k4,k5, and k6.

In rank 1, a first vector among DFT vectors of W1 may be selected usingW2 PMIs 0 and 2 and phase shift between polarized antenna groups may berepresented by 1 or −1. In addition, granularity of phase shift may beenhanced or a vector selector of W1 may be configured using k1 and k2k.

When k1 and k2 are set to 1 and 3 in order to enhance granularity ofphase shift, the phase shift in rank 1 may be represented by 1, −1, −j,and j.

When k1 and k2 are set to 8 and 10 in order to set a vector selector,the phase shift in rank 1 may be represented by 1 or −1 and a firstvector or a third vector may be selected from a DFT vector of W1.

Alternatively, when k1 and k2 are set to 4 and 6 in order to set avector selector, the phase shift in rank 1 may be represented by 1 or −1and a first vector or a second vector may be selected from a DFT vectorof W1. When (k1, k2) is set to (4,6), two DFT vectors with a highcorrelation can be selected compared with the case in which (k1, k2) isset to (8,10). That is, when a channel is slowly changed in a time orfrequency domain, (k1, k2) may be set to (4,6), thereby enhancingfeedback accuracy.

Next, W2 subsampling of 4 Tx codebook in the case of rank 2 will bedescribed below.

k3 and k4 may be set to 0 and 1, respectively so as to include 8Txcodebook subsampling, and the following values may be considered withrespect to k5 and k6.

A first vector may be selected from a DFT vector of W1 using W2 PMI 0and 1 in rank 2, and phase shift between polarized antenna groups may berepresented by 1 with respect to a first layer and represented by −1with respect to a second layer or maybe represented by j with respect toa first layer and represented by −j with respect to a second layer. Inaddition, a vector selector of W1 may be set using k5 and k6.

When k5 and k6 are set to 4 and 5 in order to set a vector selector,phase shift in rank 2 may be represented by (1, −1) or (j, −j) and afirst vector or a third vector may be selected from a DFT vector of W1.

Alternatively, when k5 and k6 are set to 2 and 3 in order to set avector selector, phase shift in rank 1 may be represented by (1, −1) or(j, −j) and a first vector or a second vector maybe selected from a DFTvector of W1. When (k5, k6) is set to (2,3), two DFT vectors with a highcorrelation can be selected compared with the case in which (k5, k6) isset to (4,5). That is, a channel is slowly changed in a time orfrequency domain, (k5, k6) may be set to (2,3), thereby enhancingfeedback accuracy.

In addition, k3, k4, k5, and k6 may be set to 0, 2, 4, and 6,respectively to fix phase shift of two layers to (1, −1) and fourselectors may be set. That is, when k3, k4, k5, and k6 may be set assuch, first, second, third, and fourth vectors may be selected from aDFT vector of W1.

Various values other than k1, k2, k3, k4, k5, and k6 described in theaforementioned example may be considered and an eNB may semi-staticallyset the values to a UE via high layer signaling (e.g., RRC signaling).That is, in order to reduce feedback overhead, the eNB and the UE maydetermine various codebook subsampling methods and the UE may determineone method to the UE.

Fifth Embodiment

A fifth embodiment of the present invention relates to a codebooksubsampling method when the following 4Tx codebook is used.

A CSI reporting type may be set to one of various types. For example, aCSI reporting type defined in LTE release-10 will now be described. Type1 reporting supports CQI for UE selection sub-bands. Type 1a reportingsupports subband CQI and second PMI feedback. Type 2, Type 2b, and Type2c reporting supports wideband CQI and PMI feedback. Type 2a reportingsupports wideband PMI feedback. Type 3 reporting supports RI feedback.Type 4 reporting supports wideband CQI. Type 5 reporting supports RI andwideband PMI feedback. Type 6 reporting supports RI and PTI feedback.

Hereinafter, when the following 4Tx codebook is used, a W1 subsamplingmethod will be proposed.

The following subsampling method may be applied to type 5 reporting andtype 2c reporting in submode A and submode B of PUCCH feedback mode 1-1.The following codebook W1 may set a codeword up to n=0, 1, . . . , 7 soas to constitute one W1 with dense DFT vectors in order to ensure highperformance in a correlated channel environment. In addition, thecodebook W1 may set a codeword up to n=8, 9, . . . , 15 so as toconstitute one W1 with dense DFT vectors in order to ensure highperformance in an uncorrelated channel environment.

4 Tx codebook may be represented by multiplication of two matrices asfollows.

W=W ₁ ·W ₂  [Equation 51]

Here, the inner precoder W₁ and the outer precoder W₂ may representwideband/long-term channel properties and subband/short-term channelproperties, respectively. W₁ may be set as follows.

$\begin{matrix}{{W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n = 0},1,\ldots \mspace{14mu},15} & \left\lbrack {{Equation}\mspace{14mu} 52} \right\rbrack\end{matrix}$

Here, X_(n) may be set as follows.

                                     [Equation  53]$X_{n} = \left\{ {\begin{matrix}\begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{2n} & q_{1}^{{2n} + 1} & q_{1}^{{2n} + 2} & q_{1}^{{2n} + 3}\end{bmatrix} & {{n = 0},1,\ldots \mspace{14mu},7} \\\begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{2{({n - 8})}} & q_{1}^{{2{({n - 8})}} + 2} & q_{1}^{{2{({n - 8})}} + 4} & q_{1}^{{2{({n - 8})}} + 6}\end{bmatrix} & {{n = 8},9,\ldots \mspace{14mu},15}\end{matrix},\mspace{20mu} {q_{1} = e^{2\pi \; {j/16}}}} \right.$

The codebook W₂ for rank 1 may be set as follows.

$\begin{matrix}{{{W_{2} \in C_{2}} = \left\{ \begin{bmatrix}Y_{1} \\{q_{2}^{m_{r\; 2}}Y_{2}}\end{bmatrix} \right\}},{q_{2} = {{e^{2\pi \; {j/8}}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \begin{matrix}\left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{3},e_{3}} \right)} \right\} & {{m_{r\; 2} = 0},2,4,6} \\\left\{ {\left( {e_{2},e_{2}} \right),\left( {e_{4},e_{4}} \right)} \right\} & {{m_{r\; 2} = 1},3,5,7}\end{matrix} \right.}}} & \left\lbrack {{Equation}\mspace{14mu} 54} \right\rbrack\end{matrix}$

In addition, the codebook W₂ for rank 2 may be set as follows.

$\begin{matrix}{\mspace{79mu} {{{W_{2} \in C_{2}} = \left\{ \begin{bmatrix}Y_{1} & Y_{2} \\{q_{2}^{m_{r\; 2}}Y_{2}} & {{- q_{2}^{m_{r\; 2}}}Y_{2}}\end{bmatrix} \right\}},{q_{2} = {{e^{2\pi \; {j/8}}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{3}} \right)} \right\}}},\mspace{20mu} {m_{r\; 2} = 0},2}} & \left\lbrack {{Equation}\mspace{14mu} 54} \right\rbrack\end{matrix}$

Here, e_(n) is a 4-element selection vector with all zeros except forthe n^(th) element with 1.

It is effective to perform subsampling of W1 by reflecting theaforementioned properties of W1. That is, when 4-bit W1 is subsampled to2-bit W1, a codeword up to n=0, 1, . . . , 7 is subsampled in order toensure high performance in a correlated channel environment. In thefuture, when an eNB and a UE are gradually miniaturized and the numberof antennas is increased to reduce an antenna interval, a correlatedchannel is formed with high probability if possible. Accordingly, it maybe effective to subsample a codeword up to n=0, 1, . . . , 7.

Alternatively, when 4-bit W1 is subsampled to 2-bit W1, a codeword up ton=8, 9, . . . , 15 is subsampled in order to ensure high performance inan uncorrelated channel environment. When a specific telecommunicationprovider installs an eNB with a wide antenna interval, this subsamplingmethod is advantageous.

Alternatively, when 4-bit W1 is subsampled to 2-bit W1, some codewordsof n=0, 1, . . . , 7 and some codewords of n=8, 9, . . . , 15 aresubsampled in order to ensure high performance both in an uncorrelatedchannel environment and a correlated channel environment. For example,only an even number n may be subsampled to configure a codeword.

The eNB may transmit information about one of the aforementioned W1subsampling methods to the UE. In detail, a W1 subsampling method may bedetermined using information added for CSI process configuration. Inaddition, when various subsampling methods are present for W2, the eNBmay signal information about the methods to the UE.

Sixth Embodiment

LTE release-12 has discussed introduction of a new codebook of a dualcodebook structure in order to enhance performance with respect to ranks1 and 2 of 4 Tx codebook and use of legacy release-8 codebook withrespect to ranks 3 and 4.

In ranks 1 and 2 of 4 Tx codebook, PMI information applies a dualcodebook structure in the form of W1 and W2, and thus PUCCH feedbackmode 2-1 for 8 Tx codebook may be used without changes. FIG. 18illustrates PUCCH feedback mode 2-1 according to a PTI value. Referringto FIG. 18, a wideband W1 is present with periodicity of 8 subframes inPUCCH feedback resource with offset 1 and periodicity 2 and a widebandW2 and CQI are present in the remaining resource. RI and PTI are setwith periodicity 16 and offset 0. When PTI is set to 1, L-bitinformation indicating subband W2 and subband CQI, and a subband indexis reported as shown in FIG. 16.

However, in the case of ranks 3 and 4 of 4 Tx codebook, PMI informationapplies a single matrix codebook structure configured with W instead ofa dual codebook structure in the form of W1 and W2. Accordingly, it isdifficult to use the PUCCH feedback mode 2-1 of FIG. 18, for supportinga dual codebook, without changes. For example, in the case of ranks 3and 4, a value of PTI is not necessary.

Hereinafter, two feedback methods will be proposed in order to supportPUCCH feedback mode 2-1 for ranks 3 and 4 in 4 Tx codebook.

In a first feedback method, a feedback framework of feedback mode 2-1 ischanged according to rank.

According to the first feedback method, PUCCH feedback mode 2-1 in ranks1 and 2 uses a legacy method as illustrated in FIG. 18, and PUCCHfeedback mode 2-1 in ranks 3 and 4 may be set as illustrated in FIG. 19.Referring to FIG. 19, PMI information W and wideband CQI may be presentwith periodicity of 8 subframes in a PUCCH feedback resource with offset1 and periodicity 2 and L-bit information indicating a subband CQI andsubband index is present in the remaining resource. RI and PTI are setwith periodicity 16 and offset 0. That is, the feedback framework offeedback mode 2-1 may be changed according to rank.

When a UE determines and feedbacks a PTI value in ranks 1 and 2, an eNBinterprets the PTI value as an effective value to determine a type. Onthe other hand, the UE may determine and feedback PTI=0 or PTI=1 inranks 3 and 4. When RI indicates rank 3 or 4, the eNB does not interpretand disregards the PTI value. Alternatively, the UE always fixes andfeedbacks PTI=1 and the eNB also recognizes the value. Similarly, the UEalways fixes and feedbacks PTI=0 and the eNB also recognizes the value.

When RI re-indicates rank 1 or 2, the UE determines and feedbacks a PTIvalue and the eNB does not disregard the value and interprets the valueto determine a type.

In a second feedback method, a selectable PTI is limited according torank.

According to the second feedback method, PUCCH feedback mode 2-1 inranks 3 and 4 may be configured as illustrated in FIG. 20. Referring toFIG. 20, a wideband W and a wideband CQI are present with periodicity of8 subframes in a PUCCH feedback resource with offset 1 and periodicity 2and L-bit information indicating a subband W, a subband CQI, and asubband index is present in the remaining resource. RI and PTI are setwith periodicity 16 and offset 0.

When the L-bit information indicating the subband W, the subband CQI,and the subband index is reported, W2 needs to be subsampled similarlyto the case of 8Tx so as not to exceed the size of a payload of PUCCHformat. In ranks 3 and 4, CQI is 7 bits and L is a maximum of 2 bits,and thus 2-bit subsampling may be performed with respect to ranks 3 and4 as shown in one of Tables 12 to 14 below.

TABLE 12 RI W2 values 1 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} 2 To Be Determined 3 {0, 2, 8, 10} 4 {0, 2, 8, 10}

TABLE 13 RI W2 values 1 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} 2 To Be Determined 3 {1, 3, 9, 11} 4 {1, 3, 9, 11}

TABLE 14 RI W2 values 1 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15} 2 To Be Determined 3 {4, 5, 6, 7} 4 {4, 5, 6, 7}

One of Tables 12 to 14 above may be set via a 2-bit subsampling methodof W2.

The UE and the eNB may determine W1 as an identity matrix and the UE UEmay select and signal W2 in a single codebook of ranks 3 and 4.

In the case of ranks 1 and 2, like in a conventional method, when the UEdetermines and feedbacks a PTI value as 0 or 1, the eNB interprets thevalue as an effective value to determine a type. On the other hand, inthe case of ranks 3 and 4, the UE always determines and feedbacks PTIas 1. When RI re-indicates rank 1 or 2, the UE determines and feedback aPTI value as 0 or 1, and the eNB interprets the value to determine atype.

With reference to FIG. 21, a method for reporting channel state (CSI)according to an embodiment of the present invention will be described.

In operation S211, a UE subsamples a codebook for a 4 antenna port.

A detailed subsampling method is the same as a method for subsamplingthe aforementioned codebook for ranks 3 and 4, and thus a detaileddescription thereof will be omitted.

In operation S213, the UE feedbacks CSI based on the subsampledcodebook.

For example, the CSI may include a rank indicator (RI) reported togetherwith a precoding type indicator (PTI), and when an RI is greater than 2,a PTI may be set to 1.

With regard to the channel state information transmitting method of FIG.21, the aforementioned various embodiments of the present invention areindependently applied or two or more embodiments are simultaneouslyapplied and descriptions of redundant parts are omitted for clarity.

In addition, the same idea as that proposed by the present invention canalso be applied to uplink MIMO transmission and reception for MIMOtransmission between a BS and a relay (in backhaul uplink and backhauldownlink) and MIMO transmission between a relay and a UE (in accessuplink and access downlink).

BS and UE to which Embodiments of the Present Invention are Applicable

FIG. 22 is a diagram illustrating a BS 110 and a UE 120 to which anembodiment of the present invention is applicable.

When a relay is included in a wireless communication system,communication in backhaul link is performed between the BS and therelay, and communication in access link is performed between the relayand the UE. Accordingly, the BS or the UE illustrated in the drawing maybe replaced by a relay as necessary.

Referring to FIG. 22, the wireless communication system includes a BS2210 and a UE 2220. The BS 2210 includes a processor 2212, a memory2214, and a radio frequency (RF) unit. The processor 2212 may beconfigured to embody procedures and/or methods proposed by the presentinvention. The memory 2214 is connected to the processor 2212 and storesvarious information related to an operation of the processor 2212. TheRF unit 2216 is connected to the processor 2212 and transmits and/orreceives a radio signal. The UE 2220 includes a processor 2222, a memory2224, and an RF unit 2226. The processor 2222 may be configured toembody procedures and/or methods proposed by the present invention. Thememory 2224 is connected to the processor 2222 and stores variousinformation related to an operation of the processor 2222. The RF unit2226 is connected to the processor 2222 and transmits and/or receives aradio signal. The BS 2210 and/or the UE 2220 may have a single antennaor a multiple antenna.

The embodiments of the present invention described hereinbelow arecombinations of elements and features of the present invention. Theelements or features may be considered selective unless otherwisementioned. Each element or feature may be practiced without beingcombined with other elements or features. Further, an embodiment of thepresent invention may be constructed by combining parts of the elementsand/or features. Operation orders described in embodiments of thepresent invention may be rearranged. Some constructions of any oneembodiment may be included in another embodiment and may be replacedwith corresponding constructions of another embodiment. It is obvious tothose skilled in the art that claims that are not explicitly cited ineach other in the appended claims may be presented in combination as anembodiment of the present invention or included as a new claim by asubsequent amendment after the application is filed.

In the embodiments of the present invention, a specific operationdescribed as being performed by the BS may be performed by an upper nodeof the BS. Namely, it is apparent that, in a network comprised of aplurality of network nodes including a BS, various operations performedfor communication with a UE may be performed by the BS, or network nodesother than the BS. The term ‘BS’ may be replaced with a fixed station, aNode B, an eNode B (eNB), an access point, etc.

The embodiments according to the present invention can be implemented byvarious means, for example, hardware, firmware, software, or combinationthereof. In a hardware configuration, the embodiments of the presentinvention may be implemented by one or more application specificintegrated circuits (ASICs), digital signal processors (DSPs), digitalsignal processing devices (DSPDs), programmable logic devices (PLDs),field programmable gate arrays (FPGAs), processors, controllers,microcontrollers, microprocessors, etc.

In a firmware or software configuration, the embodiments of the presentinvention can be implemented by a type of a module, a procedure, or afunction, which performs functions or operations described above.Software code may be stored in a memory unit and then may be executed bya processor.

The memory unit may be located inside or outside the processor totransmit and receive data to and from the processor through variousmeans which are well known.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the invention. Thus, it isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

INDUSTRIAL APPLICABILITY

The above-described embodiments of the present invention can be appliedto a wireless communication system such as a user equipment (UE), arelay, a base station (BS), etc.

1-14. (canceled)
 15. A method for transmitting a channel stateinformation (CSI) by a user equipment (UE) in a wireless communicationsystem, the method comprising: determining a precoding type indicator(PTI) and a precoding matrix indicator (PMI) based on a rank indicator(RI); and reporting the CSI including the PTI, PMI and the RI to a basestation (BS); wherein if the RI is greater than 2, the PTI is equal to 1and the PMI is restricted to use 4 precoding matrices out of 16precoding matrices in a codebook, and wherein the 4 precoding matricesare as follows: ${W_{0} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}},{W_{2} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}},{W_{8} = {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}}},{and}$ $W_{10} = {{\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}}.}$
 16. The method according to claim 15, wherein the CSIis transmitted using a physical uplink control channel mode 2-1.
 17. Themethod according to claim 15, wherein a payload size for reporting thePMI is 2 bits.
 18. The method according to claim 15, wherein each of the4 precoding matrices is a 4 by 4 matrix.
 19. The method according toclaim 15, wherein when the RI is 3 or 4, a final PMI is determined asthe PMI, and wherein when the RI is 1 or 2, a final PMI is determinedusing the PMI and another PMI.
 20. A user equipment for transmitting achannel state information (CSI) in a wireless communication system, theuser equipment comprising: a radio frequency (RF) unit; and a processoroperably coupled with the RF unit and configured to: determine aprecoding type indicator (PTI) and a precoding matrix indicator (PMI)based on a rank indicator (RI); and report the CSI including the PTI,PMI and the RI to a base station (BS); wherein if the RI is greater than2, the PTI is equal to 1 and the PMI is restricted to use 4 precodingmatrices out of 16 precoding matrices in a codebook, and wherein the 4precoding matrices are as follows:${W_{0} = {\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}},{W_{2} = {\frac{1}{2}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}}},{W_{8} = {\frac{1}{2}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}}},{and}$ $W_{10} = {{\frac{1}{2}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}}.}$
 21. The user equipment according to claim 20, whereinthe CSI is transmitted using a physical uplink control channel mode 2-1.22. The user equipment according to claim 20, wherein a payload size forreporting the PMI is 2 bits.
 23. The user equipment according to claim20, wherein each of the 4 precoding matrices is a 4 by 4 matrix.
 24. Theuser equipment according to claim 20, wherein when the RI is 3 or 4, afinal PMI is determined as the PMI, and wherein when the RI is 1 or 2, afinal PMI is determined using the PMI and another PMI.